You are arching in the middle of every L-sit pull up. Watch yourself on the way down, it is clear as day to me. Watch your lower chest and you will see it too. This is often caused by both not using the lower lats (the part that connects to the pelvis) and by not having good scapular control. Think traps and serratus anterior. Your glenohumeral muscles (deltoids, rotator cuff, etc) are having to try and pick up the slack, but they can't control the shoulder blade so they can't keep your humeral head from gliding around in the socket (because it is the socket that is moving around, it is part of the shoulder blade).
If you concentrate on keeping hollow, even if it's with bent legs at first, I think you will find that your problems go away. You will also get stronger. This is very important.
Your regular pull ups are also quite arched, which is probably where the movement fault originated. You can't just change from arched to hollow without practice ![]()
It is much harder to see what's going on in the L chins, but the externally rotated position moves the largest part of the humeral tubercles (the bony lumps where rotator cuff muscles attach, between which the long head biceps tendon runs) out of the way and this may be why you are not feeling any issues with them. I think the previous bit about staying hollow probably appies to them as well.