Try
searching the NTSB's accident database.
I assume you're talking about special LSA (S-LSA) and not experimental LSA, since most of those should be converted "fat" ultralights (Yes, I know, the -12 can be E-LSA, but at the moment, there aren't any AFAIK). If you search for "light sport", you get 97 entries. Most of these are E-LSA and some are certified aircraft with the words "light sport" present in the narrative. Looks like about 40 or so S-LSA incidents / accidents.
Lots of landing / takeoff incidents, which is consistent with my understand of LSA handling characteristics, particularly for mid/high time pilots who are transitioning to LSA with their low momentum in the flare and light weight (affecting crosswind and gusty wind operations). A few fatilities, some of which are stall/spin, some of which are fuel starvation, some of which are unknown.
I would say that the landing / directional control on the ground type of accidents are of interest since there are so many. Most LSA don't handle the same in the flare or on the ground as spam cans, so pilots who transition from them to LSA are going to need some extra time to transition. I think this will be reflected in insurance rates for LSA shortly - time in type will count a lot more than total time.
I'm recalling my first landing in a 172, which came after 160 hours in LSA and in about 10kt of wind. As I flared the airplane and it ploped in, I started laughing. "What?" says my instuctor, thinking something's wrong. "That's it?" I say. Easy in comparison to every LSA I've landed.
Now, getting to your point about medical issues. I don't know of a LSA accident that was determined to be due to a medical issue that would have disqualified them from a medical. There certainly may be some, but I just don't know of them.
I do know of recent glider accidents (one of them fatal) that were medical related, but remember, gliders operate under different rules even than LSA - no medical is required, nor is a driver's license. PIC is required to certify that they can fit to act as PIC and complete the flight in a safe manner (sorry, don't have the exact FAR off the top of my head).
My opinion is that transition training and proper landing technique in the flare are the biggest problems facing LSA safety right now. Stall/spin awareness is the second. Training (both students and CFIs) can do a lot to address the first and second. Stall warning horns might help with the second - most LSA don't have them, and for students, stall horns can help give yet another cue that a stall is approaching.
TODR