liom SOMETIMES means "with me". The entry for le in the FGB says that it can correspond to " With; to, for; by, against" in English, depending on the circumstances that it is used in.
Some examples where liom definitely isn't the equivalent of "with me" in English:
cara liom - "a friend of mine"
chuir sé an madra liom - "he set the dog on me"
Ná bí liom mar gheall air - "don’t annoy me about it"
Is liom féin é - "it is my own"
Éist liom - "listen to me"
There are quite a few comments on that at the discussion about the other sentence "Taitníonn sé": https://forum.duolingo.com/comment/4296658/Taitn%C3%ADonn-s%C3%A9 I hope that will answer your question. :-)