My cams captured one near confrontation when the lion ran away as a coyote approached. In fact, every time I watched that section of the video, I thought that it looked as if the mountain lion was pouncing toward something rather than simply fleeing. I wondered if there was a coyote just outside the field of view of the camera who the lion was going after. (this clip is in today's video too).
Now, I am even more curious about that question because this coyote showed up nearby just after the chase. Note that he is not weighting his right hind leg at all. He headed for a birdfeeder and began eating birdseed off the ground.
It's a hard life for the wildlife. I suspect that, unless the hind-limb healed miraculously fast, the injured coyote might not have make it, especially in the cold of winter. Moreover, the mountain lion risked his life to take down such a huge prey animal and then did not get all the nutrition from it as he could have due to the coyotes.
However, one key fact that always helps me to deal with the sadness that a prey animal was killed is that every last scrap of that elk was eaten by the lion or a scavenger. During the days, the carcass was covered in ravens, magpies, and Stellar's jays. By night, the coyotes kept working on the nearly bare skeleton even when it looked like it was stripped clean.
It's the cycle of life unfolding before our eyes. It's not always easy to watch but it's how the world works.