If you are planning to conduct your own blood lactate test then try to make the testing modality as event specific as possible. A treadmill will work fine but do not be constrained by that. If you have a 3-4 min hill that you can skin or ski walk up with poles, you can do several repeats with 10 bpm increases each lap up this and collect the sample at the top. I did this sort of test for years with skiers and feel it delivered actionable information.
As for your questions:
running or walking/ski stride simulations is your choice as to which you want to test
Slope choice will again be dictated by trying to make this event specific.