Just remember, Your Vizsla doesn't have to be able to outrun the Cougar, she just has to be able to outrun you. ;D
All silliness aside, no domesticated dog, of any breed, alone, stands a chance against a full grown mountain lion. In groups of two or more the odds will swing in their favor. The other factor is that mountain lions don't fight to fight, except each other for territory and breeding. They would most likely quielty move off. Even Lili is a much harder target than a rabbit, squirrel. or a domesticated cat.
If you're running in an area where there have been Mountain Lion sightings. Your chances of meeting one are really, really slim.
I know that everyone remembers the story about the Mountain bikers in The Cleveland National Forest( California) that were attacked and killed, but it's an odds on bet that at some point in those cats lives someone(s) tried to domesticate them, and when they found they couldn't control them any longer they set them free. I lived, and trained( cross country runner) in that area as a kid, running hundreds of miles and never saw a Mountain Lion.
If your going to run in that area with Lili, just use her as an early warning system. However, if your are running in an area where you have such concerns, I'd find another area to run in. Personally I'd be more concerned about the two legged creatures than the four legged ones. Be safe.