Flatting my horse before lesson?

Yeah why not Hop on her and just get her listening to your aids in walk and maybe a little bit of trot. Get her moving off the leg and reacting to your forward and back aids, then leave it at that. You don't want to wear her out before your lesson.
Otherwise, just pop her on the lunge for a few minutes before you get on, ask for lots of transitions up and down and within gaits to get her cued into you and working her back.

hmm ok sounds like a plan

I like to be on Nelson about 15 minutes before my Coach shows up for my lesson, so that we are already warmed up when she arrives, and that we don't have to waste 20 minutes of our precious lesson time, on warming up.

I ask for alot of forward energized movement at the walk, long and low and do alot of bending work - shoulder in's n out's, leg yiedling, serpentines and all that good stuff. By the time my Coach is there, we are ready to do trot and canter work and jumping.

There's nothing wrong with doing a good warmup before your lesson so that you are both ready for the real work when your Coach is ready

Absolutely yay, and I think the above two posts put it well. My horse is in training and often they have me warm him up before we ever get to a lesson. The other day it was spring weather and windy and the trainer had me lunge him first because he was all stall hyper. Only for a few minutes though, not a long time because you want energy for the lesson.