We store our lard in the fridge/freezer. I have also had beef tallow, and it seems to keep fine at room temp, but I have had lard go rancid at room temp for too long. You can tell it is rancid, because it reeks really bad. lol
Lard is supposed to last a year at room temperature and two years in the fridge. I think if it's not very well rendered and has trace bits of food in it and/or the room is extremely hot as like 90 something degrees for awhile, it can go rancid quicker. The freezer should preserve it even longer. I keep mine in the fridge.
If you are getting alot, you can store it long-term in the freezer. Otherwise, it's fine at room temp. in a cabinet or something. This is how my mom has used it for years (like 40 years, and no one has gotten sick yet!).