Punish non movers

I'm 1600 player, playing 5min blits and having to deal with such situation every day:
I have 4 pawns advantage or more and my opponent stops moving for the rest of the game. Can lichess make some hard fouls for this kind of behavior?

yes

I'm dealing with the same problem

when i as 1000 player play 1min blits i got angry, two.
but i had idea! just stop moving peaces before him.
he can not stop moving because not his turn.
works 100%

If he times out, its free ranking. I would just sit through it.

Sometimes players just quit the game after a couple of moves and I have to wait for 4.5 mins...

There are automatic temporary bans for people who repeatedly sit on their clock.