One thing you can add to your bag of tricks when you come upon a mountain lion is to use your wind breaker or other piece of clothing to look big. Raise your jacket, full sail, above your head. Again, do not run. It's that wacky killer instinct that they just cannot control when prey runs. Dogs, while usually mindful of others, do have a wild streak within.
Runners can be likely targets.
Pooches won't get lost or injured, others won't have to encounter a dog they do not know, and all are happy. If bitten, get the owner's name and phone number. Clean the injury very well and watch for infection. A tetanus shot is recommended. Do not hesitate to alert local authorities.