LP Loss/Gain Should Somewhat Reflect How Well You Performed
As in, let's say you go 4/1 toplane, but your midlane feeds their ass off to an Irelia who is now 6/0 by 10 minutes, resulting in a loss. There is no reason why you should lose anywhere near the same amount of LP they do.
Or how about you're playing adc and you play awful, not positioning well not warding and just feeding, but your jungler is 10/0 and you get carried. You should not earn the same amount of LP they do, they should earn more than you.
One of the things that is frustrating to me is when I perform very well in a game, but we still lose because of teammates that underperform, afk, ragequit, run it down, etc. I would feel more like I am earning my place in rank if my LP gain/loss actually reflects on how well I performed in a match, I think this is fair. If I lose I should lose LP, but if I lost the game because my midlaner ragequit, or my jungler just consistently fed before the laning phase was done, I shouldn't be punished to the same extent if I at least performed well.
op.gg creates an "OP Score" for you every match, which is defined as "A rating system that measures a users performance within a game by combining stats related to role, laning phase, kills / deaths / damage / wards / damage to objectives etc.". It's in beta, but I feel it does a pretty good job. Riot already tracks all of these things which you can see in the stats page at the end of the game.
As far as I know, you lose/gain LP based on the probability that your team was going to win/lose the match (I could be wrong this is just what I have heard). I would rather not earn/lose LP based on a bet that I would win or lose, but rather on how well I performed in my role.