I would not imagine those tips are getting burnt if they're so far from the lights, but I have no experience with artificial lights so that's just a guess based on the picture.
I have seen that sort of thing on a different species of stapeliad, and some tips seem to die back for whatever reason (none in particular that I can identify beyond the general downturn that tends to happen here during our annual summer drought).
I suppose I could have studied that phenomenon and figured out why it happens, but I have opted not to and just accept tip dieback as an occasional part of the plant's lifestyle. It tends to branch prolifically. So even though not all of those branches have an equally bright future, the number still keeps going up over time.
