I have been in on several successful lion hunts in NM. We were hunting for a particular lion each time (for ranchers), in an area where there are very seldom lions, so it may not apply.
We would first find sign (kills etc.) in various locations, then try to determine how old it was. From this we would put together an idea of the cat's range and try to determine how long a time it took him to "make a circuit" around his range area.
Once we had an idea of where is "circuit" was, and how long it took him to make his way around it (several days to a week or more), we would try to be ahead of him in a good hide, waiting. We did use prey sounds when we knew he had gotten into the area, usually lost lamb, fawn, or calf.
This involved sometimes a week of scouting, aided by info from the ranchers. We'd usually get our hide set in the afternoon and spend the night there, hoping to get a shot in the morning.
My hunting partner, Pat, is very good at this, and has been hunting that country for 55YRS. Even so, there were times when we misjudged and had a cat pass us in the night. I have waited in a hide for a day and a half before getting a shot. We were also busted a couple of times, which usually worked out OK for the ranchers, since the cat would then generally move on to a completely new area.
Big cats can be a real challenge. They are not very scent sensitive, but ANY motion will alert them. They seem almost to have a sixth sense, and sometimes seem to be able to tell that they are being hunted, even from long distances where you know you cannot have been busted yet.