Yes. I like how Google translate wrote it when translating the Spanish version; "the cat's son is a kitten; the son of the lion, cub".

Oh yeah! Definitely better.

Definitely better than puppy, but not quite specific to lions.

It’s specific to lions, just not exclusive to lions.

Ooh, pedantry, my kind of thread:

https://en.m.wiktionary.org/wiki/specific

I think it fails on most if not all definitions of specific.

"Lion cub" is specific, lion and cub are both specifiers. But "cub" is specific to juveniles of a range of species; so I'd say "not specific to lions".

Interesting then to think which species do have specific English single-word names for juveniles. Owlets, foals, and joeys spring to mind ...

French has louveteau for a wolf cub, perhaps it has a specific lion cub word too? I'd imagine Kiswahili to have a specific word, perhaps?