I looked a bit online and found some for sale but before I clicked the buy button...
If this is just for a fun experiment then just go for it. No need to ask for input first. Test it and report the results.
If you are seriously looking for a firearm lubricant, then there are countless much more accessible and much more suitable products.
Let's assume there are no gun stores in your area.
Let's assume you don't have access to the internet--or maybe that you have some reason not to shop online.
Let's assume you don't have access to any automotive parts/product stores.
Let's assume you don't have access to any department stores like Wal-Mart.
Let's assume you don't have access to any hardware stores.
Let's assume there are no convenience stores or gas stations in your area that carry any lubricants.
Let's assume there are no mechanic shops or small engine repair shops or car dealers that might sell you some oil.
Let's assume you can't order some kind of oil using your phone and a credit card.
Let's assume your grocery store doesn't have a hardware section with any lubricants or a pharmacy that carries things like mineral oil.
At this point, I'm wondering how you got a gun and where you plan to get ammunition for it, what happens if your car breaks down or needs an oil change, but let's just pretend...
You could still go to a grocery store and find a plethora of products that would work just as well, and probably far better than bear fat.
Things like shortening, lard, butter, margarine, vegetable oils, nut oils, cooking sprays, etc. would all be cheaper and easier to get than bear fat and work at least as well. In a pinch, you could even buy some fatty meat and render the fat yourself, or maybe buy some nuts and press them for oil to make a lubricant.
I'm a big experimenter. I probably have around 20 different oils and greases on hand at the moment from testing I've done with firearms, but even I think there's a point where things just don't make sense any more.