although my log doesn't go back to when i first started working on it, if i recall it really doesn't take that long (relative to beasty skills like the front lever and planche). i started out doing tuck-sits on the edge of my bathtub, and once those were at around 10 seconds i moved to L sits. I really didn't go about them in the best way-going to failure too often. I found that just improving overall mid-section strength and stability (planks in my case) along with some hip flexor work (knees to elbows/knee raises/leg raises) did the trick. I hadn't really tested an L sit for the better part of a year, and just doing the above exercises my L-sit went from a rough 8-10 sec last fall to a decent 15 sec now.
that said, if you want to get an L-sit, the best/fastest way is to just do it. Start off working on tuck sits, train them frequently (but allowing recovery days), and go for total time. So try to avoid failure for the most part. Set a workout goal of, for example, 30 sec, and then do small, doable sets until your total time is there. Eventually, it will take you fewer sets to hit your time goal, and then eventually you can progress to an L-sit. Probably when you can do a tuck sit for 10-20 seconds i imagine. I rushed and jumped into L sits before i was ready to make the most of my beginner progress so i'll just say to be patient.
soo i suppose that was a bit more than you were asking for, and since i never gave you a true time answer, i'll now say that you should be able to have an L sit in 1-4ish months depending on where you're starting, how hard you work, balancing recovery, etc...very roundabout i know, but i hope that helps
