Does "They don't have a life" sound correct?

As he and I walked past a group of individuals, my rude friend said:

They don't have a life.

I hadn't heard the expression before that. Does it make sense?

They were individuals (plural) but he said "life," which is singular. Shouldn't he have used "lives"?

They don't have lives.

Solution 1:

Assuming they are good people living there, obviously they do have lives. But since it's your rude friend mocking them, I believe what he meant is that they're boring.

"They don't have a life" is grammatically okay. And it's a variant of "They need to get a life!".

Get a life! — Cambridge

something you say to a boring person when you want them to do more exciting things.
"Don't tell me you're cleaning the house on a Saturday night? Get a life, Hannah!"

Solution 2:

"Having a life", et al, is a class of idioms for having friends, interests, and other reasons for "wanting to get up in the morning".

A person that "doesn't have a life" is presumably getting up, going to work, coming home, doing laundry, then going to bed, with little else beyond eating, being depressed, and perhaps some TV and Internet browsing. (Stack Exchange excepted, of course!!)

But in particular the imperative expression "Get a life!" is used to imply that the target person has so little "life" in the above sense that he is meddling in stuff he should stay out of, or is being critical of things he knows nothing about.