Depends on where you’re going. My husband killed his lion while deer hunting. His father shot one in the paw with a judo point once when it kept approaching him in his tree stand. Both were in Montana. Several people over the years have killed lions in self defense while hunting but couldn’t keep them because they didn’t have a tag. What’s the lion population like where you’ll be?
If you can legally (as its archery season) and will carry a sidearm or rifle, maybe. The odds that you’ll get a broadside shot a calm cat have to be almost nil. I certainly wouldn’t want to try and shoot one of those things head on with a bow if I didn’t have to.
Also, what’s your cost? If it’s $20ish (resident), no big deal, pick it up. If you’re getting close to $100 (non resident) or more I’d probably rather buy a bunch of raffle tickets and try and get a sheep or goat tag.
For me as a resident a $29 mtn lion tag is a no-brainer. The last time I had an archery deer tag I had a lion dead to rights at about 40 yards but no mtn lion tag. Never again, though it was only the 3rd I've seen in the daytime in nearly 40 years.
If you're a non-res $104 may be a little steep on the very slim change you see a lion.
Hunting mountain lion is a lot of work. The chance of you seeing one while out deer hunting is less than 10%. Most of the time, they know you are there but you have no clue where they are at. Their hearing and eyesight are extremely sharp and they smell very well. They can see in the dark having a lot of rods in their eyes. They will be there but you will only see one once in maybe every 10 hunts. You should go on a targeted cougar hunt with someone experienced with them. You almost have to find a kill site and then track the cougar down. I am not an advocate of guided hunts, but if you want to hunt mountain lion, I would recommend you find a guide to take you on the first hunt and show you the ropes of it. Cougar is great eating and tastes kind of like pork.
To make my prior comment clear, the odds of seeing one are small. I have shot only one in my entire lifetime and I am 63. It's not worth the investment unless you specifically hunt that animal deliberately and it requires different tactics than just sighting them. I am a Colorado native and had a rancher offer to pay me $500 to hunt one. I turned him down because my cost would be much higher. I counter offered $2000 per season plus $500 per lion I took down and permanent, irrevocable permission to hunt the ranch for my entire lifetime. He turned me down.
One of my dad's friends regularly hunted lions and he did it with dogs. Even then it's a ton of work. I never rode a horse so many miles in my life. My limbs were so stiff when I got back to camp, all I can do is lay on my cot and groan. Even with an expert cougar hunter, it took us 6 days to locate the mountain lion my dad's friend was paid to hunt.
Depends on the state, depends on the price. I have bought tags in Montana and Wyoming in the past, and will again. Probably should always have one in Arizona while coues deer hunting as well. Cant say for sure about Nevada, since that state hates my applications and I never have hunted there. If I ever get to deer hunt Nevada, I'll likely buy a lion tag as well.
Hunting style and the country you'll be hunting are other considerations. If you're spending a lot of time behind glass...may be worth it.
I've seen 30+ lions while out hunting over the years and could have killed over half of those if the season would have been open, I had a tag, or was a legal animal (female with no kittens).
You know after seeing a few more comments and actually looking on the Wyoming G&F website, the license only being $32 for me (resident), I may get one. I for one will be doing a ton of glassing and basically walk and stalk. The terrain I am hunting in is mostly rolling hills, sandstone and limestone formations and a lot of shale slopes with steep sides, benches, a few small mesas draws and fingers. There is a lot of deer, mostly whitetail, where I am hunting so that being primary prey of these here cougars, it's not a whole lot of loss if you don't fill the tag, but having tasted cougar meat before, I would probably cry a few tears if I glassed one and had no tag. So I am going to qualify my answer. Check with the game and fish in the state where you are hunting and talk to a game biologist. Try to get an idea what the population of mountain lion in your area is. They will not give you specific clues on where to go, but they will give you options and answer population questions. Compare the cost to the odds which is likely somewhere around 10-15% odds and maybe higher if the deer population is on the high side. If you think it's worth it, buy the license. I know I am after I did some more research.