I am not all that conversant with the wiring schematic for the K100LT, but it could be an issue in the ignition or kill switch.
A couple years ago, I had problems with my K75RT shutting down on me suddenly while riding. In my case turning off the ignition and turning it on again brought back normal running most of the time. Finally, the engine wouldn't start no matter what I did. Disassembling the ignition and cleaning the internals brought back proper operation, and I haven't had any problems in the 30,000 miles since.