Didn't think about it in my first post, but I lived near Homedale, Id, when I went lion hunting with a friend who is a guide and owns a game farm near Parma.
The rules in Idaho may have changed since then (I moved from Idaho about nine years ago), but he carried a .22RFM.
I was much more concerned about bears because I am an avid trout angler. Bears like to wait for you to land a trout or start cleaning your catch and then go after your fish.
I carried a Glock 20 loaded with 200-grain hardball. Carrying 16 rounds of hot 10mm ammo made me as confident as I could get with a pistol. I see you list an Elite Match in 10 in your signature. That would be my back country carry gun.
Unless you are hanging around in Owyhee County, I suspect bears are more of an issue than lions.
But, since you are in Boise, I suggest you go over to Intermountain Outdoor Sports and find an old guy behind the gun counter and ask him what works best on the local backwoods predators. If his name is Ron S., take his word as Gospel.
The dog suggestion is a good one for lion protection. I'd recommend a cur, a Jack Russel or a rat terrier. They are all very quick and agile, have excellent noses and great ears. They won't win a fight with a predator, but they will give you more warning than almost any other breed. Then it is up to you.
In Idaho, you must remember that it is OK to kill predators to protect livestock, but it is not to protect pets. So, if you must shoot something out of season it is because your life was threatened, not your dog's...
I miss Idaho. If I ever go back it will be to the Owyhees, somewhere near CDA or near Pocy. The Owyhee River Canyon is one of the last great "undiscovered" places in the country.