The short answer is lubricant. You would want to avoid using anything sticky or thick. If the oil is sticky it will collect dust and form a cluster of crud that will, as you say, gum up the lock. But that's not going to happen instantly, and the crud can generally be cleaned out if it happens.

If the key is hard to get into the lock, that means the pins aren't sliding up easily. You need to get lubricant into the pins. That means you need a spray lubricant, unless you want to pull the lock, disassemble it, clean it, lubricate it and put it back.

You can use WD-40 or spray graphite, or frankly, just about any other spray lubricant; locks are not a super-high-tech device where very specific lubricants are necessary. Just don't use anything thick. I use WD-40, but some locksmiths swear by graphite. Graphite isn't sticky, but in my view it's not as effective a lubricant. Also, the carrier for spray graphite is not as good at clearing out any crud that has already gummed up the lock (if any).

Bottom line: good old WD-40 would be fine. It's nothing more complicated than a light machine oil in a volatile carrier. The carrier carries the machine oil into all the crevices, then evaporates, leaving a thin layer of machine oil, which is exactly what you want. Push the thin tube into the lock, not very far (certainly not all the way to the end), and give it a few short squirts. Some of it will run out, so make sure you have some paper towels and maybe some rubbing alcohol to clean off the drips.

Wait a few seconds, then push the key in and out to work the oil into the pins. The key should feel easier to push in right away. If it doesn't, then lubrication is probably not your problem, but you can try a few more squirts and working the key a bit more. If it loosens, great. If it doesn't, you can do the whole disassembly and cleaning thing, but you're probably better off replacing the lock at that point.