Remember, this was used long before refrigeration was a thing. I know Crisco used to sell a lard, and it would sit on the shelf (with a plastic lid on it) for several months before it went bad. It had to be kept covered for sure, and over time it does go rancid - sniff test will let you know when it's past its prime. I used to make biscuits with it, you "cut it in" with the flour. Lard was also used (for example, in a mason jar) to store cooked meat. It would keep the meat from spoiling. (Place the cooked meat in a jar, pour in melted lard to the top, cover). I personally never used it to store meat so don't trust me on the details of that, I only saw a video once.

I have a container of beef tallow that we bought at Feldmans (farm and home supply store) that just hangs out in the cool pantry. Been there for a year and it’s still fine lol

eh, how cool is your pantry?

Storing in the fridge is best, but if your pantry is a cool one (cellar, outside, etc) I imagine that would be ok.