For what it's worth, here's my translation of the pertinent section in the letter to Menoikeus:
127f. Ἀναλογιστέον δὲ ὡς τῶν ἐπιθυμιῶν αἱ μέν εἰσι φυσικαί, αἱ δὲ κεναί,
- Ἀναλογιστέον "consider..."
- τῶν ἐπιθυμιῶν "of the desires, yearnings"
- "Consider then of the desires, on the one hand, are the φυσικαί "natural ones'
- φυσικαί (physikai)
- English physical, physics
- on the other, the κεναί 'empty, fruitless, vain, void ones."
- κεναί is also again the word used when Epicurus talks about atoms and void.
127g. καὶ τῶν φυσικῶν αἱ μὲν ἀναγκαῖαι, αἱ δὲ φυσικαὶ μόνον·
- "And of the natural ones, on the one hand, are the necessities; on the other hand, the natural ones only."
- ἀναγκαῖαι "necessary, essential; (if a plural noun as here) necessities"
127h. τῶν δ᾽ ἀναγκαίων αἱ μὲν πρὸς εὐδαιμονίαν εἰσὶν ἀναγκαῖαι,
- "then, of the necessary ones: on the one hand, there are those necessary for eudaimonia;
Those necessary for eudaimonia are open to interpretation but must be based on Epicurus's philosophy.
127i. αἱ δὲ πρὸς τὴν τοῦ σώματος ἀοχλησίαν, αἱ δὲ πρὸς αὐτὸ τὸ ζῆν.
- ἀοχλησία "freedom from disturbance"
- σώματος genitive singular of σῶμᾰ
- σῶμᾰ "the body; one's material body or existence"
“then, those [necessary] for the freedom from disturbance for the body; then those [necessary] for life itself.”
There are some translations that interpret αἱ δὲ πρὸς τὴν τοῦ σώματος ἀοχλησίαν to mean only things like clothing and shelter - those things that provide "freedom from disturbance" for the body, that is for one's physical existence. That isn't literally what is written so that is simply one interpretation. Those kinds of things - clothing and shelter - would seem to fall under the final category of those necessary for life. So, this category should catch those between eudaimonia and those necessary for life. This is an interesting category.
I would contend that those "necessary for life itself" are those essentials at the base of Maslow's hierarchy of needs: food, water, shelter, sleep, air, etc. Again, clothing and shelter would seem to fall into this category.
PS. It's important to remember that this categorization tool deals with desires for something. I realize it's hard to distinguish between desires for specific pleasurable outcomes or activities and the pleasurable outcomes or activities themselves. I find it difficult myself. To provide a different way of reading that section with additional context adding in the word desires instead of just "ones" and "those":
Furthermore, on the one hand, there are the natural desires; on the other, the 'empty, fruitless, or vain desires.' And of the natural desires, on the one hand, are the necessary desires; on the other, the desires which are only natural; then, of the necessary desires: on the one hand, those desires necessary for eudaimonia; then, those desires necessary for the freedom from disturbance for the body; then those desires necessary for life itself.