I agree that Lola's loose powder is good. I haven't tried La Mer's loose powder though, I have tried the creme foundation sample and it is really good if you are looking for a natural make up.
I have never try La mer loose powder,But in my experience,Don't use shiny loose powder.... I tried Shiseido,kose....both are terrible!
I use Covermark for many years which is soft,natural and its powder is very fine.Highly recommended!