It would seem there is no "Q" source, only the LXX used as template! Observe=
-Luke 24:13 = Two [δυο] disciples are walking along when a disguised Jesus asks why they are dejected. At verse 18 Cleopas remarks to the interlocutor that he "must be a sojourner/out-of-towner" [παροικεις] if he isn't aware of the recent events in Judea's capitol.
-Genesis 19:1= Two [δυο] angels stay with Lot.
-Luke 24:20= Cleopas explain that "our rulers gave Jesus the death-sentence/judgement" [εις κριμα θανατου]
-Genesis 19:9a= the Sodomites tell Lot: "You came here as a visitor/sojourner [παροικεις], not to sentence us like a judge [μη και κρισιν κρινειν]."
-Gen 19:15b= angel tells Lot: "Be not destroyed along with the lawless [ανομιαις]!"
-Luke 24:7= Jesus was crucified by "sinful [αμαρτωλων] men"
-Luke 24:8= "They remembered [εμνησθησαν] his sayings."
-Gen 19:29= "...God remembered [εμνησθη] Abraham and sent Lot out from the catastrophe's midst..."
-Gen 19:9= the men "approached [ηγγισαν]" Lot's home and in verse 11 they are "stricken with blindness" [αορασια] (cf. Luke 24:23= women claimed to "have seen" [εωρακεναι] angels—a reversal)
-Luke 24:15b-16= Jesus "approached [εγγισας]" the two but: "they're eyes were kept from recognizing him." (=literally: "they did not know [μη επιγνωναι] him")
=compare also Gen 19:8 Lot has two girls who "have not known [ουκ εγνωσαν] a male"
-Luke 24:16, like Gen 42:8 has "doesn't recognize", while Luke 24:35 echoes Gen 45:1 which describes Joseph as "being made known (to them)"
-Genesis 43:23 = after revealing his identity, Joseph says to his brothers: "Peace be unto you, fear not!", which Luke 24:36-37 rewrites as Jesus materializing out of nowhere to say to his disciples: "Peace be unto you!" but they "were frightened" due to this.
-Gen 45:9 = Joseph tells his brothers to "Ascend unto my father [αναβητε προς τον πατερα μου]!" and in line 13 he asks that his "glory" [την δοξαν μου] be reported.
-Luke 24:26= Jesus mentions his own "glory" [την δοξαν αυτου] in the third person.
-the author of the gospel of John uses this reference in his presentation of his version of the Resurrection story= John 20:17= Jesus instructs Mary Magdalene: "Go to my brothers and say: 'I ascend [αναβαινω] unto my father [προς τον πατερα μου].'"
-Like Joseph's brothers in Genesis, the disciples at Luke 24:52 "do obeisance" before departing.
-Gen 19:19= Lot asks the angel a favor: "Since I've found [ευρεν] grace with you, (in order) that I might live [ζην]..."
-Luke 24:23-24= there are "ones who say he (=Jesus) is still living [ζην]" while some others—going to check it out—"found [ευρον] it as they'd said [ουτως καθως]"
-Luke 24:29a= journeying a while with Jesus, Cleopas and his unnamed companion "pressured him [παρεβιασαντο αυτον], saying, 'Remain with us [μεινον μεθ' πμων], for it's near evening [οτι προς εσπεραν εστι] and the day has declined.' [και κεκλικεν η ημερα]'"
-Gen 19:3 Lot ""constrained them [κατεβιαζετω αυτους]... and they entered [και εισηλθον] into his house [εις τον οικον αυτου]." (=cf. Luke 24:29b= "He entered [και εισηλθε] to stay with them.")
-Gen 19:1= "Two angels entered Sodom at evening [εσπερας]."
===we'll save the discussion for a later time, but Luke is making clear that he as a sacred scribe is aware of how Biblical stories borrow form eath other= The Sodom story of Bereshith 19 was rewritten as Judges 19, the bizarre tale about the murder of the Levite's whore. Luke, by mentioned how "the day declined" is referencing Judges 19:9= For behold, the day has declined, being evening." [ιδου, δη κεκλικεν η ημερα εις εσπεραν] (see also= -Luke 24:32= "Wasn't our heart [καρδια] on fire as he was speaking [ως ελαλει ημιν] to us on the road?" = compare Judges 19:3= "The husband rose up and went after her to speak [λαλησαι] unto her heart [επι την καρδιαν αυτης].")
-Luke 24:31= at the exact instant the disciples recognize Jesus, he becomes invisible!
-Gen 19:2 = "And (Lot) said: 'Behold [ιδου] lords [κυριοι], turn aside here... to wash your feet [νιψασθε τους ποδας υμων]—that rising early tomorrow you may go forth on your way [εις την οδον υμων]."
-Luke 24:35= "They described the things (that happened) in the way [εν τη οδω]..."
Luke 24:38-39= Jesus invites his followers to: "Behold [ιδετε] ... these feet of mine [τους ποδας μου]!" (= cf. how verse 39b he exhorts them to "Handle/grab me!" [=like the impertinent Sodomites?] and in verse 40 he "displays [επεδειξεν] his (crucified) hands...")
-note how Peter + the 3 women are basically equivalent to Lot + wife + 2 daughters ('Magdalene' = 'tower' = i.e. pillar of salt perhaps?) — at any rate, the evangelist makes this connection by reversing a sentence from Genesis=
-Gen 19:17= και εγενετο ηνικα εξηγαγον αυτους εξω
-Luke 24:50-51= εξηγαγε δε αυτους εξω ... και εγενετο
(=also Luke 24:50 has "by the hand" [τας χειρας αυτου] like Gen 19:16's three pointed mentions of hands.)
-Luke takes the theme of disbelieving from Lot's story and transforms it into that of the women-witnesses, not using exact words this time, though=
-Gen 19:14b= Lot tries to warn his daughters' fiancees, but: "He seemed to his sons-in-law to be kidding/joking around before them" [εδοξε δε γελοιαζειν εναντιον των γαμβρων]
-Luke 24:11a= the rest of the disciples doubt tales of resurrection: "it apeared before them to be as if a wives' tale (literally= 'vain/trifling reports')" [εϕανησαν ενωπιον αυτων ωσει ληρος τα ρηματα]
-Luke 24:12= Peter: "rising up [αναστας], (quickly?) ran [εδραμεν] to the tomb... (then) went forth [απηλθε] to his own (house) wondering [θαυμαζων] about what had taken place [το γεγονος]."
-Gen 19:15= "They quickly [δε εσπουαζον]... 'Rise up!' [αναστας] ... to go forth [εξελθε]..."
-Gen 19:21= the angel: "was in wonder [εθαυμασα] ... over those words of yours [επι τω ρηματι τουτω]... concering which you spoke [περι ης ελαλησας]..."
-Luke 24:10= "the ones who spoke [αι ελεγον] these things [ταυτα]..."
-Luke 24:22= "Some women [γυναικες] from among us [εξ υμων] ... happened upon (the tomb) at dawn [γενομεναι ορθριαι]"
=the above re-works and re-uses the idea of (but not the precise vocabulary as) Gen 19:15= "It happened at dawn [ηνικα δε ορθρος εγενετο] ... (that the angels instructs Lot to:) 'Rise up and take your woman/wife [γυναικα]..." (=note how Luke 24:46b echoes this again by bringing up how Christ being "raised" [αναστηναι])
-Gen 19:12b= concerned angels ask Lot if he has friends/family "in the city" [εν τη πολει] who might also wish to evacuate.
Luke 24:49= in one of those usual New Testament 'reversals of theme,' Jesus admonishes the opposite: "Stay in the city [εν τη πολει], until ... you receive ... power from on high [εξ υψους]!"
-Gen 19:13 explains that Sodom is to be obliterated because the "cries/protestations" of those wronged by its inhabitants "has been raised up on high (or: 'to the heights')" [υψωθη]
====minor, but still definite, allusions to Gen 19 in Luke24====
-Luke 24:12 = the linen bands "alone" [μονα]
-Gen 19:8= Lot tells Sodomites to "leave these men alone [μονον]!"
-cf Luke 24:18= "Are you visiting here alone [μονος]?"
-Luke 24:17= a disguised Jesus approaches two supposed strangers: "And he said to them" [ειπε δε προς αυτους]
-Gen 19:7= Lot: "said to them [ειπε δε προς αυτους], 'By no means, brothers, do (such) wicked (things)!'
-Luke 24:19= Jesus inquires: "What (are the) kind [ποια] of things (occurring recently)?"
-Gen 19:5= Sodomites cat-call: "Where are they [που εισιν], the men [οι ανδρες]...?"
-Luke 24:19= Jesus is called "a man [ανηρ] who did mighty deeds and speeches before all the people [παντος του λαου]" (= compare Gen 19:4b= "all the people, before [απας ο λαος αμα]" Lot's home.)
-Luke 24:30 = Gen 19:3b, just not the same vocabulary in Greek.
-note how much alliteration is occuring in Luke 24:28b= "he pretended to be going further" [προσεποιειτο πορρωτερω πορευεσθαι]
-Luke 24:33= "They returned [υπεστρεψαν] to Jerusalem (=a reversal of Lot's wife looking back to her doom?] and found gathered together [συνηθροισμενους] there..." (=like the Sodomites on Lot's lawn?)
-Gen 19:17= "Don't stand in any adjacent place..." = Luke 24:36= Jesus "stood in their midst..." (=a reversal)
-Gen 19:20 = Lot twice calls Zoar a "small place" = is this the reason Luke 24 calls the place the 2 disciples travel to a "town" [κομων / κωμην]
============= Genesis 1-4 allusions by Luke =====
-Gen 2:21-22= the Lord God put Adam "into a change of state [εκστασιν επι τον αδαμ]... and made a rib he took from [απο του] Adam into a woman [γυναικα]." (cf verse 23b= "She'll be called 'Woman' [γυνη] since she came from [οτι εκ] man.")
-Luke 24:22= "Some women [γυναικες] from among [εξ υμων] us amazed us [εξεστησαν] ..." (=by claiming angels told them etc)
-Gen 2:23= "Now this is [τουτο νυν] bone of my bone [οστουν εκ των οστεων μου] and flesh of my flesh [σαρξ εκ της σαρκος]."
-Luke 24:39= Jesus says: "A ghost doesn't have [ουκ εχει] flesh [σαρκα] and bone [οστεα] like you view me as having."
-Gen 1:1 = "In the Beginning [εν αρχη]..."
-Gen 1:2 = "darkness upon the face of the Deep [αβμσσου] and God's spirit bore upon [επεϕερετο] the water [επανω του υδατος]"
-Gen 1:5 = "There was evening then morning—the first [μια] day."
-Luke 24:1= "day one [μια] of the week, at deep dawn [ορθρου βαθεως]..."
-Luke 24:1= "bearing/bringing/carrying [ϕερουσαι] the spices/perfumes..."
-Luke 24:27= "then, beginnning [αρξαμενος] with Moses..."
-Luke 24:51= "And it was (so) [και εγενετο] while blessing them that [εν τω ευλογειν αυτον αυτους] he was parted from them [διεστη απ' αυτον] and was carried aloft into heavem [και ανεϕερετο εις τον ουρανον]."
-Luke 24:50b = "He blessed them" [ευλογησεν αυτους]
-Gen 1:6= "Let there be a parting/division [διεχωρισεν] between water and water..."
-Gen 1:15b= "God said: 'Let... (such and such be) ....' And it was (so) [και εγενετο ουτως]!" (=cf. ibid at vv. 9, 11b, 24b, 30b)
-Gen 1:28a = "And he blessed them [ευλογησεν αυτους]" (cf v. 22)
-Gen 1:29b = "(Here) there is to you foods/edibles!" [εσται εις βρωσιν]
-Luke 24:41b = Jesus asks: "Have you anything edible here [εχετε τι βρωσιμον ενθαδε]?"
-Gen 1:26 = "Let mankind ... have control over [αρχετωσαν] the fishes [των ιχθυων] ... and the winged creatures [των πετεινων]..."
-Luke 24:42 = "They gave over to him a portion of roasted fish [ιχθυος] and some honeycomb from bees." (=winged creatures?)
=Luke sprinkles in some Gen 4, skipping ahead for his allusions=
-Gen 4:26b= It is explained of Seth's son Enosh: 'This one [ουτος] hoped [ηλπισεν] to call upon YHWH's name (as God)."
-Luke 24:21= "We we hoping [ημεις δε ηλπιζομεν] that this one (Jesus) was [οτι αυτος εστιν] the one about to ransom Israel."
-Gen 4:14b-15 = Cain declares: "All who find me [ο πας ευρισκων με] will kill me [αποκοτενει με]!" But God puts on him "a mark/sign to not [μη] do away him, for those who discover [ευρισκοντα] him."
-Luke 24:23= "And did not [μη] find [ευρουσαι] his body [το σωμα αυτου]."
-Gen 3:24= a flaming sword is posted to "guard the way" [την οδον] to the tree of Life.
-Luke 24:32= "Wasn't our heart burning within us on the way [εν τη οδω]?"
-Gen 3:19= "By the sweat of your brow you shall eat your bread, until returning [αποστρεψαι] from the ground you came from!"
-Luke 24:33= "They returned [υπεστρεψαν] to Jerusalem."
-Gen 3:21= "God made for Adam and his wife shirts of skin, and he clothed [ενεδυσεν] them."
-Luke 24:49= Jesus commands his followers to remain in the capitol city "until such time as you will be clothed [ενδυσησθε] with power from on high."
-Gen 3:20= "Adam called the name [το ονομα] of his wife, Zoey, because she was mother to all [παντων] the living."
-Luke 24:47= "His name [τω ονοματι] shall be proclaimed ... unto all [παντα] the nations... for forgiveness of sins [αϕεσιν αμαρτιων]."
-Gen 4:7= "You sinned?" [ημαρτες]
-Gen 4:13 = Cain says: "My fault [αιτια μου] is too great to (ever) forgive me [αϕενηναι με]!"
-Gen 4:6 = God asks Cain: "Why is your face downcast [συνεπεσε]?"
-Luke 24:17 = Jesus asks bystanders what they converse about while "walking [περιπατουντες] and looking dowcast [εστε σκυθροποι]"
-Gen 3:8= "They heard the voice of the Lord GOd, who was walking [περιπατουντος] ... at dusk [δειλινον]." (=is this why Jesus is 'walking' apparently close to 'sunset' in Luke 24?)
-Gen 3:17= "This alone [τουτου μονου] I told you [σου] not to eat."
-Luke 24:18 = "Are you alone [συ μονος]?"
-Gen 3:8b = the humans hid from God "In the midst [εν μεσω] of the paradise tree"
-Luke 24:3b= "Jesus (magically materialized? and) stood in their midst [εστη εν μεσω αυτων]
-Gen 3:3= Even tells the snake she isn't even supposed to "touch/handle" [αψησθε] the fruit of a certain tree.
-Luke 24:39 = Jesus invites onlookers: "Touch/handle me!" [ψηλαϕησατε με]
-Gen 3:6b= Eve: "having taken [λαβουσα] the fruit ... she gave some [εδωκε] also to her husband, and they ate [και εϕαγον]."
-Luke 24:30b= "having taken [λαβων] the bread ... he gave some [επεδιδου] to them."
-Luke 24:31 directly quotes Genesis 3:7, concerning the 'fruit' from the Life Tree= "and their eyes were opened and they knew..." [see below=]
-Luke 24:31= αυτων δε διηνοιχθησαν οι οϕθαλμοι και επεγνωσαν αυτον
-Gen 3:7= και διηνοιχθησαν οι οϕθαλμοι των δυο και εγνωσαν
-Gen 42:29= returning to Jacob, the 10 brothers "report (on) all that [απηγγειλαν αυτω παντα] occurred"
-Luke 24:9= women who found empty tomb "report all these things" [απηγγειλαν ταυτα παντα]
-note how Luke 24:22 has εξεστησαν while Gen 45:26 has εξεστη.
-Gen 41:31= "the famine ... was strong/severe" [του λιμου ... ισχυρος]
-the above line is echoed by Luke 15:14 where the 'prodigal son' leaves home because "there began to be a severe famine" [εγενετο λιμος ισχυρα]
-the nameless older brother of Luke 15:30 (a figure obviously meant to represent 'Jews' supplanted now by new 'Christians') makes the accusation that his little brother has been "with whores" [μετα πορνων], a vague reference to Judah (the original 'Jew'—the group is named after this figure!) who in Genesis 38:15 and 22-23 calls his daughter-in-law Tamar this term, ironically after lying "with her" during a ruse. In Luke 15:29 the elder brother complains that his younger sibling has been rewarded for nothing while he and his "friends" didn't even get "a goat" [εριϕος] in return for loyal service. This same word for 'goat' is used three times in LXX Genesis 38:17, 20, and 23 where Judah's "friend" Chiram tries to pay the disguised Tamar whom he thought was a prostitute.
