When does the lease actually expire?

Legally, until the lease expires, yes you absolutely can insist that they continue to pay rent until replacements are found (though in return, you would be expected to expedite the process of finding those replacements), up until the lease expires.

Mind you, "insist" and "actually make them do so" are not the same thing. You might end up having to take them to court to get that money out of them.

...

OTOH, if the lease is up next week, and they didn't sign a renewal ... you're out of luck, unfortunately.

But I am not a lawyer.

You need to speak to one, to be absolutely sure of anything.