My opinion for playing fast is not just stamina. It is timing between your fretting and picking hands. If you are comfortable with scale positions and can play them without thinking too much about them and you have good hand streght built, the key is to have the timing down between the hands. Any run you want to play should be started by practicing slowly and working up to speed. Very few people can grab a guitar and play to speed.

When I was learning the Ozzy/Rhoades lead for 'I Don't Know' by ear many years ago, there is a little ascending run in the middle that was, for me, harder than it sounded. Once I figured out the notes, I couldn't seem to find the run comfortable to do out of the box even though most leads I could do after figuring them out. So, I just work on it slowed down to make the movements comfortable for me and worked up to speed from there.

I think that once your hands reach a certain strength, it's a matter of know where you are going on the fret board and practicing the timing.