I have not heard of anyone trying to do that kind of repair. I assume that the warranty has expired?
I have not had any problems with my Luxos U, but once I was rather curious to know more about it and after doing a few internet searches I found this link:
https://groups.google.com/forum/#!topic/randon/qob5ex7lrWgThe first post on date 6/15/16 has several photos of the inside. In that post, when he mentions capacitors, I suspect he really means tiny Li Ion batteries. Other posts in that thread may also help you figure out the best plan of attack, as that is the only discussion I have seen on the internet about fixing a Luxos U.
I have essentially zero skill at soldering tiny connections on circuit boards, but on a few occasions where I could cut a wire and solder a new wire to the old wire instead of messing around with a circuit board, I was successful.
Good luck.