The smallest mammal (Etruscan shrew) is about the same size as the largest ant (Driver ant Queen). You probably need to speed up the tiny-lion metabolism, but in general the mammal body plan can work around that size.
On the other hand, to scale up insects to the size of a lion, you would need to completly redesign the respiratory at least and the entire exoskeleton construct will also be pushed to it's structural limits.
Downscaling mammals is much more realistic then upscaling arthropods.
Yeah well... "giant" ants still aren't lion sized. Or even cat size. Perhaps "oh wow that's a big ant" big, but not actually that... big.
The fossils indicate that the males grew up to 3 centimetres (1.2 in) and the queens grew to 7 centimetres (2.8 in). It had a wingspan of about 16 centimetres (6.3 in).[7][8]
Fight? I'm sure you meant "keep as a pet". And obviously the microlions. I'd feed them ground beef and try to maintain a breeding population, eventually sell them as pets.
Could an ant sized lion actually hurt you? Their teeth are built to wrap around and grip thinner pieces of the body. If they are shrunk down, I don't know how efficiently they could work their way through skin. It'd be like trying to bite a wall or something.
Don't know about that, but think how strong ants arenin proportion to their weight. If that carried through, it could probably just batter you with its legs/head.