If you loll somewhere, you sit or lie in a very relaxed position. He was lolling on the sofa in the shadows near the fire He lolled back in his comfortable chair. = lounge, sprawl
If something fairly heavy, especially someone's head or tongue, lolls, it hangs down in a loose, uncontrolled way. When he let go the head lolled sideways Tongue lolling, the dog came lolloping back from the forest