Security and Customs at BKK
 

Is there a Fasttrack lane for either Arrivals or Departures in Bangkok?

both for immigration and security for departure and immigration on arrival
for TG F and J and F/J of various airlines with fast track card
no fast track for transit security
also none for customs but there are seldom any queues in opposite to USA or Australia

There is. Make sure they give you a fast track card.

TG don't have fast track cards, other airlines do have for F and J
TG's check in for F and J has it's own fast track security and immigration; for arrival just go through TG's fast track opposite gate D4 on the right side and have the boarding pass ready if you are asked to show