Regarding the alphabetical order, I think one of the oldest alphabetically organized dictonaries extant is ‘Alphabetical collection of all words’ by Hesýchios¹. In his preface (written as a letter to a friend named Eulogios), Hesychios writes that quite a few other people in earlier times have made alphabetical collections of words, but always only for a certain subset, e.g. all homeric words, all words found in the tragedies or in the comedies etc. After them a certain Diogenianós was the first (according to Hesychios) to make an alphabetical collection of all words.²
The names of the older lexicographers Hesychios mentions are: Appíon (Ἀππίων – or Ἀπίων?)³, Apollónios son of Archibios (Ἀπολλώνιος ὁ τοῦ Ἀρχιβίου)⁴, Théon (Θέων)⁵, Dídymos (Δίδυμος)⁶.
² https://el.wikisource.org/wiki/Epistula_ad_Eulogium – “κατὰ στοιχεῖον” is the phrase meaning ‘by / according to the letter’, understood as ‘alphabetical(ly)’; “καθʼ ἕκαστον στοιχεῖον” ‘by / according to every letter’.
The names of the older lexicographers Hesychios mentions are: Appíon (Ἀππίων – or Ἀπίων?)³, Apollónios son of Archibios (Ἀπολλώνιος ὁ τοῦ Ἀρχιβίου)⁴, Théon (Θέων)⁵, Dídymos (Δίδυμος)⁶.
¹ https://en.wikipedia.org/wiki/Hesychius_of_Alexandria
² https://el.wikisource.org/wiki/Epistula_ad_Eulogium – “κατὰ στοιχεῖον” is the phrase meaning ‘by / according to the letter’, understood as ‘alphabetical(ly)’; “καθʼ ἕκαστον στοιχεῖον” ‘by / according to every letter’.
³ a search turned up https://en.wikipedia.org/wiki/Apion
⁴ certainly https://en.wikipedia.org/wiki/Apollonius_the_Sophist
⁵ I donʼt know, https://en.wikipedia.org/wiki/Aelius_Theon perhaps?
⁶ a search turned up https://en.wikipedia.org/wiki/Didymus_Chalcenterus