Oooh, I love questions like this. Let's see, 2005 LT, new noise, more rumble than rattle, noticed only when front brake lightly engaged and rpm <2000 (I'm guessing) and mph < 5 and clutch engaged (tranny not under load) and seems to come from low center right hand side (but might be from elsewhere). I wish you had the bike to check out a couple of things. First I'd look for vibration caused by loose mounting bolts on the front fender (this has more of a rattle sound, but it's a quick and easy rule-out). Then I'd look for loose mounting bolts that attach the center stand and the side stand. While I was at it I'd look to see if the heat shield over the exhaust pipe was loose. Once those had been ruled out I'd put the bike up on the center stand, put it in neutral, start it up (well ventilated space!!! eye protection, gloves, long sleeves, all safety precautions) and crawl around to see if I could hear the noise. If yes, it's likely to be engine related, if no it's unlikely to be engine related. Then I'd put it in first gear (clutch engaged), put some rubber bands around the left grip and clutch lever to hold the lever in, and crawl around again to see if I could hear/isolate the noise. Then I'd double check to make sure the rear wheel was not touching the ground, take off the rubber bands, keep the bike in first, and let the rear wheel rotate at idle speed while checking for the noise. Then I'd pull in the clutch, rev the engine a bit, slowly let out the clutch, let the rear wheel rotate faster, pull in the clutch, rubber band the lever, and crawl around while the residual momentum of the rear wheel was turning the rear drive, shaft, and tranny output shaft. I'd pay particular attention to the rear drive, U-joints, and tranny. Get a cardboard tube, or roll up a piece of thin cardboard, and use that as a stethescope; put one end right on the rear drive and listen; then move it to the rear U-joint position, then the front U-joint position, then to the tranny. You may have to repeat the procedure to get the rear wheel moving faster several times to get to all these positions. By this time you have approximated most of the parameters of the bike's functioning when you hear the noise in the parking lot, except movement and front brake. Turn off the engine. Just to double check, grab the rear tire with one hand at 3:00 and one hand at 9:00 (caution!! metal parts might be very hot) and push-pull several times. There should be no play. Grab the wheel at 12:00 and 6:00 and push-pull several times. There should be no play. (I'm really hoping that it's not your final drive!) Put the bike in neutral and rotate the rear tire with your hands, listening for possible scraping of the rear brake pads.
OK, to the front. Put a jack under the front of the tranny, a piece of wood on the jack, double check to make sure the bike is secure on its center stand, and slooooowly jack up the front. The front wheel will come up off the ground. I like to continue jacking until the rear tire comes in contact with the floor; this gives the bike a 4-point stance (jack, two feet of the center stand, and rear tire) rather than a very short 3-point stance. Rotate the front tire with your hands. Listen for rumble at the front wheel bearings and front brakes. I don't know if there is any way to lightly engage the front brake and rotate the tire, I doubt you can rotate it fast enough to give you any useful data. You may want to ride the bike to the top of a small hill, turn it off (so you can hear better), and carefully roll down the hill with the front brake lightly engaged.
At this point you may have isolated the system that is involved and the location of the rumble within that system. Next steps would depend on what you have found. Hope the dealer can find it quickly and fix it inexpensively. Good luck!
'99 Canyon Red K1200 LT - Buddah Bike