Lactate Test Protocol with or without Body Core Temp taken into account?

Are you taking about actual lactate blood testing, or just approximating lactate threshold with power tests? If actual blood testing, then It’s probably a good idea to test in the ways most specific to your training and training. If you’re going to be training on the heat then it behoves you to test in the heat.

I would caution about setting zones based on a one off lactate test tho. My hr and power at LT2 vary by a fair amount (+/- 5bpm and 15ish watts) based on a lot of different factors. Really the best is to validate lactate zone by testing during specific sessions.