Seeing that you still have a significant amount of warranty time left on the system, my preference (were I in your place) would be to send it in for servicing if it really bothers you that much. As far as any potential loss/damage that might occur during shipping, I would take detailed pictures of the ENTIRE system prior to being packed up and include them with the system (of course keep a copy too!). Do NOT ship anything that is not part of the problem; i.e, remove your SSD, battery, memory, etc. and itemize what you are sending in. Provide a concise cover letter explaining the problem so that the techs know exactly what needs to be addressed. Follow all of the other recommendations provided by Lenovo or the repair center. Insure the shipment.
As far as you doing the repair yourself, the problem is probably with the LCD ribbon cable. I don't have an X200 but traditionally the ThinkLight is mounted at the end of the cable. You would have to remove the LCD bezel and pull the panel out to get at that end. You would also need to remove the keyboard and possibly the keyboard bezel to get at the end which is plugged into the motherboard. The full details can be found in the Hardware Maintenance Manual here:http://www-307.ibm.com/pc/support/site. ... MIGR-70149
Replacement LCD ribbon cable could probably be sourced from eBay. Don't know if Lenovo would sell that part by itself. Good luck!