I see that the link in my comment above goes to a cover page needing a sign up.
I have permission to post the comments on the first two lines of the pericope. Unfortunately, the formatting and pictures don't appear to paste in. I'll try to partially edit.
Probably more than you asked for but informative:
Comment
Line1 καὶ ἐγένετο ἐν τῷ ἑξῆς (Luke 7:11). The grammatical structure, subjectless ἐγένετο + time phrase (here: ἐν τῷ ἑξῆς) + finite verb (here: ἐπορεύθη), which appears in Luke 7:11, is characteristic of “translation Greek.”[3] Buth has shown that these grammatical structures are indicative of a Hebrew—not an Aramaic—vorlage representing the literary Hebrew narrative structure: impersonal וַיְהִי + setting + finite verb.[4]
Luke’s elliptical phrase ἐν τῷ ἑξῆς implies the word χρόνῳ and means “soon afterward” (Metzger, 142). The use of ἑξῆς is rare in LXX (6xx);[5] its meaning in the LXX is “in succession,” however there is no Hebrew antecedent that ἑξῆς translates. The paucity of ἑξῆς in the translation Greek of LXX stands in contrast to its frequent use by Greek authors.[6] In NT, ἑξῆς occurs 5xx, exclusively in Luke and 2 Acts.[7] The likelihood that the word ἑξῆς in Luke 7:11 is a product of Lukan redaction is, therefore, quite strong.
μετὰ ταῦτα (GR). Supposing that Luke’s ἐν τῷ ἑξῆς is redactional, we have reconstructed the reading of Luke’s pre-synoptic source as μετὰ ταῦτα (“after these things”), which frequently appears in LXX as the translation of אַחֲרֵי כֵן[8] and אַחַר הַדְּבָרִים הָאֵלֶּה.[9]
וַיְהִי אַחַר הַדְּבָרִים הָאֵלֶּה (HR). The opening phrase in L1 is difficult to reconstruct in Hebrew. The Hebraic construction, subjectless ἐγένετο + time phrase + finite verb, strongly suggests that the initial words of Luke 7:11 are based on a Hebrew Ur-text. On the other hand, ἐν τῷ ἑξῆς appears to be the product of Luke’s redaction. On the basis of the GreekReconstruction we have reconstructed the conjectured Hebrew Ur-text with וַיְהִי אַחַר הַדְּבָרִים הָאֵלֶּה (“And it was after these things”). This phrase appears in 1 Kgs. 17:17 as the introduction to the story of Elijah and the raising of the widow of Zarephath’s son. This Elijah narrative influenced the telling of the raising of the Widow’s Son in Judean Nain (see below, Comment to Line18).
Line2 πόλιν (Luke 7:11). Lindsey commented that Luke’s reference to the village of Nain as a πόλις (polis, “city”) is a Hebraism (LHNS). The LXX antecedent of πόλις is the Hebrew עִיר, which has a range of meaning spanning every size settlement, from “hamlet” to “town” to “city.”
נָעִין (HR). As a toponym, נָעִים (na‘im) appears once in rabbinic literature:
ד”א יששכר חמור גרם, מדבר בארצו מה חמור זה נמוך מכאן ונמוך מכאן וגבוה באמצע, כך בקעה מכאן ובקעה מכאן והר מכאן, רובץ בין המשפתים, אלו ב’ בקעות, בקעת פסלן ובקעת יזרעאל, וירא מנוחה כי טוב, זו תנעם, ואת הארץ כי נעמה, זו נעים.
"Some interpret Issachar is a large-boned ass [Gen. 49:14] as alluding to his territory. As an ass is low on either flank and high in the middle, so [does his territory consist of] a plain on either side and a mountain ridge in the middle. Couching down between the sheepfolds refers to the two plains, the plain of Akeslo and the valley of Jezreel. For he saw a resting-place that it was good alludes to Tinam; And the land that it was pleasant, to Naim." (Gen. Rab. 98:12; Soncino)
This rabbinic tradition clearly refers to a town in the Galilee, where Issachar’s tribal allotment was located, and is identified with the modern Arab village of Nein, located about 5.5 miles (8.9 km) southeast of Nazareth in the vicinity of Mount Tabor.[10]
Since the fourth century C.E., Galilean Nain has been identified as the site where Yeshua raised the widow’s son to life (Eusebius, Onom. 104:3). Nevertheless, it is important to ask whether this identification is correct. According to Josephus, another Nain existed in Judea in the first century:[11]
"At a village called Nain [Ναΐν (Nain)],[12] he [Shim'on the son of Gioras of Gerash—DNB and JNT] erected a wall and used the place as a fortress to secure his position, taking advantage of the many convenient caves in the gorge known as Pheretae [Φερεταί (Pheretai)], widening some and finding others already suitable as storerooms for his plunder. There too he stored the grain he had pillaged, and billeted most of his troops. His object was obvious: he was training his army in preparation for an attack on Jerusalem." (J.W. 4:511-513; Loeb; cf. J.W. 4:517)

The waters of the Perat spring flow through Wadi Kelt on their way towards Jericho. The caves along this canyon could have provided shelter to the brigands of Shimon Bar Giora's of whom the historian Josephus writes. Photograph by Todd Bolen. Photo © BiblePlaces.com
The waters of the Perat spring flow through Wadi Kelt on their way towards Jericho. The caves along this canyon could have provided shelter to the brigands of Shim’on Bar Giora of whom the historian Josephus writes. Photograph by Todd Bolen. Photo © BiblePlaces.com
Most scholars identify Pheretae with Ein Fara,[13] a spring in the Wadi Kelt,[14] where caves used as hideouts during the First Jewish Revolt and the Bar Kochva Revolt have been discovered.[15] The Nain to which Josephus referred was, therefore, probably located somewhere near the Wadi Kelt in the Judean desert northeast of Jerusalem.[16] Such a location for Judean Nain is reasonable since Shim‘on, who positioned his army in preparation for an attack on Jerusalem, would have wanted to be within striking distance. Again, this points to the western edge of the Judean desert.[17]

Tell al-Qurein, the possible site of the Nain mentioned by Josephus, and perhaps, also, the location of the Nain in the Gospel of Luke. Photo: Jeffrey Magnuson. © JerusalemPerspective.com.
Tell al-Qurein, the possible site of the Nain mentioned by Josephus, and perhaps also the location of the Nain in the Gospel of Luke. Photo: Jeffrey Magnuson. © JerusalemPerspective.com.
The Judean Nain is a good candidate for the location of Yeshua’s miracle, since Luke states that the report about Yeshua’s miracle spread throughout Judea and the surrounding area (Luke 7:17; L24-26). Scholars have sometimes accused Luke of geographical imprecision, but perhaps a better explanation for Luke’s reference to “Judea” is that Luke preserves an authentic reading from Anth. As Lindsey noted (JRL, 61), Luke 4:44 alludes to a Judean ministry without, however, describing it.[18] This may be due to the editorial activity of the Anthologizer, who rearranged the order of the stories in the Greek Translation of the Hebrew Life of Yeshua, and may thus have inadvertently obscured Yeshua’s Judean ministry.[19]
We have reconstructed with Hebrew נָעִין (na‘in) to which the Greek spelling points. The final nun ending (instead of mem) was not unusual in the Hebrew spoken and written in the land of Israel in the first century.[20