I run to work in a known mountain lion habitat. I even had the rare privilege of seeing one once although I have seen bobcats much more often.

When coworkers ask me if I feel safe back in those canyons I tell them I feel much more safe there than in my car on the highway leading to work. I'm sure statistics would back me up, even recent statistics.

I do take precautions. A mountain lion's usual M.O. is to attack from behind or above so I avoid running directly below hillsides and I even look behind occasionally. Since I'm usually commuting in the dark I have also considered wearing a rear facing light to confuse them.

Just FYI if you look around there are lots of TLB mountain lion threads with widely varying opinions.