I spent 4 months on Koh Lanta working as a “digital nomad” so got to explore the place pretty well. Internet connectivity is pretty good on the island, I guess due to its close location to the mainland, and all the way down the left of the island it seems to be pretty stable. On the right side of the island (Old Town) the internet is not great. 3G is also widely available (although annoyingly not where I lived on Prae’Ae beach). Either way, you can definitely work on Koh Lanta.