I've seen some studies that tried to quantify the effects of lions and coyotes, but it's tough to put a good number on them. It's also somewhat dependent on the habitat. Various studies I've seen shows that you have to spend huge amounts in predator control to show any small increase in recruitment and survival. That means, yes predators have an effect, but to prevent it, you'd have to spend millions in aerial shooting, trapping, poisons, etc. Certainly lions eat primarily deer, coyotes eat mostly young deer and then catch some deer when there's snow on the ground.
While it's difficult to say exactly how many fawns and adults a lion or coyote will eat that wouldn't have died anyway, what can be quanitified is a typical fawn:doe ratio in the west versus east. It's not uncommon for good farm country to support about 100-120 fawns:100 does. In south texas where I did my Master's thesis, it was more like 60ish100 in unsupplemented areas, and around 100 in supplemented (food plots, protein feed, etc). In the west, a down year will have 30:100 does, a good year 60:100, maybe 70:100. So not ony do they have lower fawn survival in the west, deer are much more dependent on good weather. Out here, it's rare for a year to be "normal". Averages are just a mean between good and bad years. There rarely seems to be a year when we get around average spring rains, summer temps and rains, then winter snows. Often it will be a nice mild winter, followed by a drought summer. Or a cool, wet summer (good for forb growth), followed by a disastrous winter. Never seem to get a warm, wet spring, cool, wet summer and a mild, dry winter to really kickstart a population.
In another part of Colorado, unit 40, the Glade Park herd, south of Grand Junction, there has been essentially no doe hunting for 20 years and the population has hardly budged. A combination of habitat factors, predators and weather just won't let up on them. That herd hasn't hit objective in 30 years and is presently about 50% of what carrying capacity would dictate.
I love mule deer, but they sure are sensitive little bastiges.