I think you have a good chance to see a lion on about any coues deer hunt in Arizona. I've seen lions, without dogs in AZ, CO, MT, ID, and WY. I've seen a total of 31 lions, only 1 using dogs.
Here's a really bad picture, through my spotting scope of one that I saw in Colorado, there were actually 2 cats this same size, but I could never get them both in the same frame.
I have a really cool video of a big tom walking up a ridge about 150 yards from me while I was quartering a 6 point bull that I shot in Montana. Didn't get any still pictures though.
Saw 3 lions in January here in Wyoming coming back from a late elk hunt. The next morning, while going back to pack out our elk, I ran into this guy, sunning himself about 1/2 mile from where we saw the 3 lions the night before.
Probably the strangest place I've seen a lion was West of Laramie, out in the middle of the prairie while hunting pronghorn...not a tree for miles and miles. Watched it work its way down an open ridge and make a few half hearted attempts to catch a couple doe pronghorn.
They are out there, and I've always been way tempted to pick up a lion tag when I hunt Arizona for elk, javelina, or coues deer...probably worth it. Spend enough time behind the glass in deer country, and you're probably going to find one.