@Helen *******
I don't know where Koh Lipe is, so I looked at it on a map. It appears to be a small island close to Malaysia, and the immigration office itself is located at a ferry station. I'm thinking the immigration office is for processing Malaysians and Thais; kinda like the ferry that's running between Mukdahon, Thailand and Savannakhet, Laos.
If that's the case, then they would not be processing the extension of stays. I don't know where the nearest immigration office would be? Maybe Satun?