Time for a math class
Lesbians = women who are only attracted to other women
He/him = male pronouns, used by men only
They/them = neutral pronouns, used by people who aren’t male or female
Lesbians =/= men
Lesbians =/= non binary
Lesbians = women
Therefore: a lesbian = can’t be a “he” or a “they”
Class is dismissed.
Prescriptive English? I thought you said this was Maths!
In seriousness, the modern distinction between binary and non-binary genders is, well, modern and non-binary (and he/him-using!) people have long been part of lesbian community and identity. It might not be linguistically convenient, but that’s the history lesson.
(Also non-binary genders aren’t always wholly distinct from “man” and “women”; gender isn’t a discrete quality.)