Mountain lakes? Mid July and later. Access to some is still limited and some have just recently melted off. You'll get better responses if you narrow down to a state first
Good advice above. July, August, September to fish mountain lakes.
I don't know much about other states, but awesome mountain experiences can be had, plus mountain lake fishing, by driving the Bear Tooth Highway and fishing some of the lakes along the top. If it looks like food and it's in front of a brookie, expect a hit.
A guided fly fishing day on the upper Yellowstone will give great mountain views all day long. A guide can be costly, but a great experience.