They look kind of Hamster-like … .
Wild animals rarely make good pets.
Could you keep one alive in a cage - probably.
Just keep them away from cliffs…
What do you call a guy with a lemming on his head?
Darn, too late…
cliff-ord? heath-cliff?
While we’re fighting ignorance, I hear that the whole cliff thing is something of a misunderstanding. Lemming - Wikipedia
As for keeping lemmings as pets, they like to dig and live underground much of the time. This isn’t entirely different from mice, but I’m not sure if lemmings would adapt as well. You certainly don’t see lemmings surviving in tropical areas like mice can and I’ve never heard of them infesting houses.
Just keep them away from Walt Disney.
That’s sound advice for most things. 
The tricky part is to keep them from walking into the rotating knives.