A t-shirt is excellent for defense.
With dogs, hold the t-shirt on the ends, and offer the dog the middle. When it latches on, circle the ends around its neck. Pull up sharply (may not be possible with a very large dog). Usually you can snap their neck.
With the mountain lion, I'd wrap the shirt around my fist, and feed it into the lion's mouth. Shove it as far down as you can, cutting off its airway.