I have not been able to drive my 3 wheeled Trimagnum with a 2002 K1200LT for quite awhile due to this problem.
Engine starts easily, idles at 1000 for 15 seconds, then idle speed drops and engine dies. I can rev the engine to higher speeds but will die at idle weather engine is hot or cold.
Drained tank and added new fuel. Cleaned and checked gap on spark plugs. Check vacuum lines for leaks.
I am an auto and motorcycle mechanic but this persistent problem baffles me.
I am quite familiar with Motronic EFI on a "stock" K1200 engine as installed on K1200RS and K1200LT.
HOWEVER, I have no idea if your 3 wheels beast has a stock engine, Throttle-bodies and ALL stock BOSCH Motronic components.
Troubleshooting these things at a distance is far from easy (without seeing , testing myself).
BUT... assuming all components are from a stock K1200LT, I would begin with this:
(1) QUESTION: do you have access to a GS911 or a dealers computer to read any fault codes?
(2) QUESTION: any modification or maintenance that was done just before problem started ?
(3) have you made a longer ride (full warm up) to check higher RPM pulling power on the road - any hesitations ?
(4) You can do some basic tests on the TVA (idle-Actuator) after you remove it from the Throttle-bodies. See attached PDF document...
(5) Check for a loose or badly plugged (not fully inserted) TVA connector. The TVA (idle actuator) is needed to maintain proper idle RPM with engine cold and warm.
See 1st photo in the PDF document for location.