"His cat likes milk."
Translation:Is maith lena chat bainne.
leis means "with him", it doesn't mean "with his".
Is maith leis bainne - "he likes milk"
is maith lena chat bainne - "his cat likes milk"
is maith leis an gcat bainne - "the cat likes milk"
is maith lena dheirfiúr bainne - "his sister likes milk"
is maith léi bainne - "she likes milk"
is maith lena madra bainne - "her dog likes milk"
is maith lena deartháir bainne - "her brother likes milk"
So the hint drop-down for "his cat" said "a chat" which makes sense from what I learned previously (A úll agus a húll.) So why does it use "lena" here? I may just be missing something, haven't been able to check the tips and notes yet for this section but its not making sense to me.
The phrase for liking something is always in the form 'is maith le', for example I like is 'is maith liom', you like is 'is maith leat', and he likes is 'is maith leis'. (Liom leat leis léi linn libh leo/ me you he she we you (plural) they). So that is why in this sentence 'le' (with) must be combined with 'a' (his) to make 'lena' in 'is maith lena' (his....likes). Hope that makes some sense!
a causes lenition when it means "his", no change when it means "her" and eclipsis when it means "their".
You can't eclipsis or lenite certain letters, so a leabhar could mean "his book", "her book" or "their book".
lena is a combined form of le and a.
liom, leat, etc are "prepositional pronouns" - a combined form of the preposition and a pronoun (mé, tú, etc). lena isn't on that list because it isn't a "prepositional pronoun" - the a in lena is a possessive adjective, meaning "his", "her" or "their", and it is combined with le (and other prepositions that end in a vowel) because it's easier to say lena than le a (there are other historical reasons behind the combination, but that's why it survived).
See https://www.duolingo.com/comment/7535233$comment_id=22596431 for some more detail.