I have never trained L-sit, but was able to hold a floor L-sit for 5 seconds today.
All I have been doing is trying to achieve full hanging leg lifts on stall bars (about 45 degree from touching the bar) and these hip flexor exercise where you are in a seated pike position and place your hands near your knees and lift your legs).
I am positive that once I've mastered hanging V to L leg lifts I am close to mastering floor L-sit.
So I don't really understand why people recommend starting with parallel bars (easier than floor) with bent knees and tighs parallel to the floor (easiest L-sit variation)? It's much easier to do hanging leg lifts (not even full ones) and seated pike leg raises! :S