YES!
Trapping can be a very effective way to manage any game. Cats are not overly intelligent and in some areas trappers have problems keeping lions out of bobcat and coyote sets. Generally lions will blow the jaws off the smaller traps and make their escape, but I know of at least one lion held in the jaws of a 1.75 coil spring. Many trappers are using larger traps for bobcats--not so much for added strength, but to increase pan area.
There would need to be a balance or I expect the hound hunters would howl as lions are no doubt easier to quickly trap to quota than to kill behind dogs.
Hound hunters have the better option in terms of pick and choose and can easily pass up a female or young lion while releasing one from a trap without harm to lion or trapper would be a dicey deal at best. I know at least one trapper who has done it many times, but it is not recommended. I'm not sure of the survival rate of the lions he released, though they all did walk away and he has some scars to prove the fool hardiness of the process. Using snares, there would be no option, the cat will be dead when the trapper finds it (unless using foot snares).
Another factor to consider is that as the wolf population expands, it may decrease the number of hound hunters willing to risk their dogs to hunt lions. I'm not a dog guy, but can appreciate a dedicated hound hunter willing to give up what he loves for appreciation of the value of a good dog and it is well established what wolves do to hounds when they can get a hold of them. This possibly could lead to decrease of the only consistent and really effective way to keep the lions in check besides trapping.
A split quota for trapping vs calling/hound hunting would be possible and once the quota for one is full, only the other method would be allowed for the season until its quota was filled as well.
I don't harbor a grudge against hound hunters and would love to hunt a lion that way sometime--though I'd need to get into a lot better shape! However, as an occasional trapper, I see no reason why an opportunity shouldn't be available to trap a lion as well.