The beaches on the southern part of Koh Lanta aren't very crowded at all. Just have to get south of Kantiang Bay. Even Long Beach doesn't get too crowded—it's so big that you don't notice the crowds too much, nothing like the major beaches on Koh Samui or Koh Phagnan.

Bamboo Bay

Long Beach
These are from last February. I spent two weeks on Lanta, fantastic island.