Diagnosis
The projector's internal temperature sensor thinks it's overheating, so it's commanding the cooling fan to run at maximum RPM to try to save the laser and electronics. This is a protective mode.
How to Fix It
The first thing to check is airflow. 1) Power the projector down completely and let it cool for an hour. 2) Unplug it. 3) Carefully inspect all the vents—intake on the side/front and exhaust at the back. Use a vacuum with a soft brush attachment to thoroughly clean every vent you can see. Make sure nothing is blocking the vents (books, curtains, walls). The projector needs several inches of clear space on all sides, especially the exhaust. 4) Check the room temperature. Is it unusually hot in the room? The projector works harder to cool itself in a warm environment.
If That Didn't Work
If cleaning the vents doesn't solve it, the internal temperature sensor might be faulty, or the thermal paste on the laser diode heatsink might have degraded. This isn't something you can fix. You'll need to note if the loud fan happens immediately on a cold start, or only after 30 minutes of use. That detail is important for the repair tech.
Heads Up
Never ignore this symptom or try to use the projector for long periods with the fan screaming. It's a warning. Continuing to use it could lead to permanent damage from overheating, like a dimmer laser or a complete shutdown. If a thorough cleaning of the environment and vents doesn't return the fan noise to its normal, variable level, it's time to call LG support.