I would tend to agree with what has been said so far as I quickly browsed the responses. It has been my business for some time to ascertain what killed a critter as my agency is legally liable for damage to agricultural products (in cases like this read: livestock - sheep, goats, cattle, pigs, etc.) by big game. Here lions are a big game species.
Some things to look for is the condition of the hide and small bones. Was the hide eaten through or skinned back? Bears tend to pull on the meat with their teeth while pushing the hide away with their paws. It ends up looking like the hide was rolled up off of the carcass. they may eat the ends of the bones, but usually want the soft stuff.
Mountain lions tend to kill by breaking the animals neck or choking it out. Eitherway there would be some trauma on the neck or head. They also tend to go in through the rib cage and eat the heart and lungs first. In this case, you probably shot the heart and/or lungs and lions are quite finicky so it might not have gone for those parts in this case. Either way it will appear as if the hide and ribs have been cut with scissors and will have been eaten along with the meat.
Dogs would have made a mess as would have coyotes and hogs. The only other thing I would think of would be bobcat. They will take down small mule deer which would be about the size of your deer as I understand things, I could be wrong. But, I don't think one bobcat would eat that much.
I'd be curious to hear back what you saw in relation to the thoughts presented here. Also, you're right about lions being all over. You have likely been seen by lions many times and had no idea they were around. Fortunately for us they have not targeted humans as a prey source or they would be eating us all the time. They are very efficient predators, but very shy of humans. I dealt with quite a few when I worked the Front Range of Colorado. They were in town on a daily basis.
RB