How old is the lamp? I've seen old projector lamps get a crusty build-up on the filament near the end of their life cycles. On one projector that was getting really dim, I turned the projector upside down to check the model number and the encrustation fell off the filament, restoring the lamp to almost-normal brightness. Removing the lamp housing to inspect the lamp and replacing it may do the same thing. Bear in mind that if this is happening, the lamp is about done, and it's safer to replace it than risk catastrophic failure. The lamp will age faster than normal if the vent slots are not kept clean (a vacuum cleaner with a soft brush works for this) or if the set is power-cycled frequently.
Two warnings: your owner's manual will tell you to shut down the set and wait an hour before removing the lamp. Check page 109 of the manual
and FOLLOW THE DIRECTIONS OR YOU MAY GET A BAD BURN. Also, NEVER touch the lamp itself with bare fingers unless you intend to dispose of it with no further use. When the lamp gets hot, skin oil will react with the special glass causing discoloration and structural weakening. That may cause it to explode! If you must handle the bulb, wear new disposable food handling gloves. The manual assumes that a lamp run to the end of life may break anyway, and treats the lamp housing as if it contains mercury-contaminated broken glass. (You may be able to save money by replacing the bare bulb in the housing, but wear gloves when handling the new bulb and be sure to polish the wire terminals if they are not shiny clean in the contact area. The old bulb is hazardous waste and must be disposed of in the same manner as fluorescent lamps.) If you change the bulb, be sure to reset the lamp hour record as described on page 110.
Another possibility is tarnished contacts on the bulb or lamp housing. Mild cases can be remedied by polishing with a clean pencil eraser - I prefer the soft white kind often found on mechanical pencils. Heavy tarnish may require the use of a Scotch-Brite abrasive pad (rougher stuff than you get on the back of a cleaning sponge).
If you have a smoker in the household, the optics may be contaminated
with tar (use a soft, low-lint cloth dampened with lens cleaner - do
not spray the cleaner directly into the set because it could get into
the electronics). This is work inside the set - it must be unplugged for at least an hour before starting to ensure all parts are cool. Do not touch the electronics - they are vulnerable to static electricity damage, and capacitors in the power supply may hold a charge for a time after the set is unplugged. Do not disassemble the optics - getting everything refocused and aligned is probably a major job without the proper tools and knowledge of the system. You may want to consider hiring a professional with LCD rear projector TV experience.
In the worst case, there is a problem with the regulation of the lamp power. Usually a fault of this nature will be detected and the set will flash an error code on its indicator lights instead of running. It can be repaired, but it's a job for a professional technician unless you want to swap circuit boards until it works (may not be any cheaper than paying somebody who has the service manual and knows how to use it).