Look at the gun's specifications. It will tell you how many cubic feet per minute, at what pressure, it runs at.
Then look at the compressor's specs. They will give several volume-ar-pressure numbers - the ones I've seen typically quote sustained volume at 90PSI for high-pressure tools and 40PSI for high-volume tools.
The compressor has to have sustained output equal to or greater then the gun requires, or you will run down the stored pressure in the tank and the gun will start misbehaving. Murphy's Law says this will happen in the exact place and time where it will make the most mess. Avoid y that situation; get an adequate compressor.
Note that there are alternatives.
Some HVLP systems are powered by turbines rather than compressors; these can't power any other air tool but are compact and quiet for their spray guns.
There are also airless spray systems, which just pump the paint into the nozzle; traditionally these weren't very good for anything much smaller than a wall but the latest generation can apply a furniture-quality finish.
There are "conversion" guns which you supply with high-pressure air which is used to produce HVLP air. These may work with older compressors that have bad low-pressure flow.
Remember that spray cans are also a kind of LP sprayer. Obviously they're more expensive per unit volume of finish applied, but you can buy a lot of spray cans for the cost of an HVLP system, and you don't have to clean them after every use. A handle that could to the can, with a simple trigger operating the spray, remotely improves the quality of the result considerably.
Finally, remember that there are other ways to apply finishes. I'm becoming a real fan of applying clear finishes with a padd rather than with a brush.