I'm not sure what you're asking.
There's only one genitive case in Irish, and the only genitive there is that masculine singular nouns are lenited after the definite article. Did you mean something else?
There are no vowels that cause lenition just because they're vowels.
The three 'a''s above are the Irish words for his, her, and their. a bhád (his boat - lenited), a bád (her boat - nothing happens, but if the noun had started with a vowel, it would add an h to the beginning: a hathair), a mbád (their boat - eclipsed)
I have a feeling that this isn't what you were asking, though. If you give some examples, I'll try again to answer your question.