That will work, use a easy expanding bullet, cats don't open bullets well.
After some wrecks and learning the hard way the best is a 22mag and I've used a 22lr a lot also, shoot them through the heart lungs and they staying the tree and bleed out and are dead when they drop.
357 and 44 mags tend to be loaded with to hard of bullets and the cat will usually fall or come down the tree alive and that is when all hell can break loose. Rolling around with hounds and a MT lion does spike the adrenaline butif you don't like a sever case of the WTH shakes doe it clean.
I have been toying with a Mt lion hunt and was wondering how a lever action 357 mag would stack up. Heard the outfitters do not want to take a chance with a wounded lion around their dogs. Do they prefer a bigger caliber ?
The lion in my avatar was harvested using a .45 acp. 230 grain Speer gold dot hp sitting on top of some Unique powder. Cut ragged holes at 30 yards out of a smith and Wesson JM series revolver. Cat was stone dead at the hammer fall. Hounds man asked for another chest shot on the ground before letting his hounds at it for reward! Neither bullet over-penetrated but did their job inside the liquid vitals. Looked like the original bullet bounced off opposite shoulder blade and got lodged in the heart lungs mess.357 lever is a good choice. I use or used I should say a .45 long colt with 250-300 grain bullets XTPs or Barnes, killed a bunch with it, Makes for good stopping power. I like something that has some stopping power in case it gets western.
22mag and lr work good and have killed lots but aren't legal in some places and don't have any stopping power
Lions are thinned skinned so just about any caliber works, to high power blows big holes in hides, hard to beat a good old 30-30 for lions