You generally do not need to cite the edition of a Latin text that's standardized. Lucretius 1.1 is Lucretius 1.1 no matter whom you're reading, so unless you're citing something for its textual variation, just cite Lucretius himself: Lucr. 1.1.
If you're citing a particular edition, place the name of the editor after citation. If the work is discussed, put the name in parentheses.
"See above, on 29.19; †magis† for malis at Lucr. 6.1150 (Martin)..."
- Martin's edition is being referenced here. Note that the purpose is textual. This is also the edition used in PHI.
Heroic Age. (Hesiod fr. 204.94-103 M-W)
- M-W refers to Merkelbach and West, who edited Hesiod's fragments in the Oxford edition, Fragmenta Hesiodea.
If you want to cite the site itself, and not a text in it, certainly check with the editor, as some places might have different requirements.
Quickly checking JSTOR I see that an article from 2010 (Pałuchowski, "La dédicace érigée à Ephèse...") in ZPE merely mentions it:
Aucue attestation archéologique (cf. Sanders 1982, 156–159 Gazetteer 10/10), pas un seul témoignage épigraphique (cf. l'index dressé aux pages 437–438 d'ICret IV et PHI on-line).
See also this 2016 article (Connors & Clendenon, "Mapping Tartaros") in CA:
The search term barathr returns 32 results from the Packard Humanities Institute Latin Texts (https://latin.packhum.org).
Additionally, how you plan on integrating it in your text will change how you present it.