Anything, as long as it works. I use synthetic engine oil.
There are two purposes for lubrication of a firearm
1) Wear
2) Function
Lubrication for wear in a firearm is not that critical. Just about anything will work. The high forces in an action are taken up by stationary parts, not ones that are sliding. Lubrication doesn't really help the stationary parts, and they also tend not to wear. As an example, consider 100,000 cycles, which is a fair bit of use.
Then look at an engine, 100,000 cycles is less than one hour of driving on the highway. And yes, those cylinders do slide up and down, metal on metal with just a thin oil coating between them.
Now for operation, that is a different matter. You need something that will keep the parts sliding past each other, keep the dirt out, and not stiffen up when it gets cold. An oil will tend to move debris out of the way, where grease will tend to keep it in place.