Diagnosis
You're right to look for it—keeping the filter clean is crucial for cooling. On the PU700R, the air filter isn't a user-serviceable part you can pull out and rinse like on some older projectors. It's a fine, permanent mesh built into the air intake system.
How to Fix It
Your maintenance is all about keeping that built-in filter and the vents clear. Here's what you do: 1) Make sure the projector is off, unplugged, and completely cool. 2) Locate the main air intake vent, which is usually on the side or front of the unit. 3) Use a vacuum cleaner with a soft brush attachment. Gently run the brush over the vent to pull dust out of the mesh. Don't press hard. 4) For the exhaust vent (where the hot air comes out), use a can of compressed air. Hold the can upright and give a few short bursts from the outside to blow dust out. Always blow from the inside out, or use the vacuum brush again.
If That Didn't Work
If you suspect the internal filter is heavily clogged (the projector is overheating and shutting down early), you've done all you can safely. The next step is to contact LG support. They can advise if it needs a professional internal cleaning, which involves opening the case—something you shouldn't attempt.
Heads Up
Never use liquids, household cleaners, or a rough cloth on the vents. And avoid running the projector in a very dusty room or on thick carpet, as that will make it suck in more debris. A clean environment is your best filter.