As I have said before, Koh Lanta is not a paradise for shoppers but the island has few small shops that are really selling unique souvenirs and gifts most of which were created by local artisans...
If you want to buy something in the south of Ko Lanta island head on two main beach - Klong Nin beach and Kantiang beach. Both have unique shops where the owners, or make products themselves or know exact origin of the goods...
On Koh Lanta East coast you will find a few shops, all located in Koh Lanta Old Town within 100 metres of each other, making shopping a a fun and easy.