What does "ei" mean here?
Based on the other answers, 'ei' is still meaning 'her', but when you have an 'al' before it you make a possessive adjective into a possessive pronoun. Thus, 'ei' = her; 'al ei' = hers.
Correct me if I'm wrong.
Would it be incorrect to say "Is it her lion?"
Not as far as I can tell
No, "al ei" means "hers".