Good thought -- the LT has what BMW calls a "Load Relief Relay" which turns off auxiliary loads such as lights when the starter is activated. The relay grounds through the starter. While this relay may be failing, the "snap" suggests something arcing. Before looking to the relay (which is in the electrical box under the tank), I'd suggest checking whether the wire from the relay which makes the relay's ground connection is loose at the starter. Randy Prade lost his lighting during a trip due to this. You can see the connection (with a flashlight) by raising the seat and looking under the frame backbone, on the rider's left.dronning said:Breakers/relays reset after a period of time. They can go bad or just become weak so they trip more easily. Do you have allot of extra lights wired in? The initial load when you turn the bike on might be pushing the limits if everything is on.
I'm not familar enough with the LT to tell you where to look for the main relay but thats where I'd look first. When I get back home I'll check out the wiring diagram.