LP balance

This is because the system feels that you should be lower than you actually are. It's no different than if it were to like.. drop you a division and a half (or whatever it feels you should be at) and then equalize the LP gain/loss. That's basically what the system thinks should happen in order for you to be in balanced matches. So if you win 50% of your games you will eventually lose LP to get to that point then it will be evened out.

Just win more games and it will put your MMR back up to where your league is (or higher, at which point you will win more LP for winning than you lose for losing)

If you can't win more than 50% of your games then the system is right, you are supposed to be lower than you currently are. If you can, then you will catch up.

This is probably due to you losing a bunch of games at 0 LP or going 2-1 or 3-2 in promos a lot since all of those losses that don't affect your current LP (because of the way the divisions work) are lowering your MMR but not lowering your league. Therefore by its formula, you shouldn't actually be as high as you are, but you weren't demoted for losing those games at 0 LP so you remain artificially higher than you should be. Which doesn't matter because the games still place you by MMR, so yeah.

One thing to remember is that the system is not designed for you to climb in tiers, it is designed to give you a 50% chance to win at any point, and place you, based on your winrate vs the other people with similar MMR, in a division and a tier at a certain LP. So it adjusts its LP gain/loss to push you where you should be. Like if you were to theoretically win exactly 50% of your games for 1000 games starting NOW, it would push you to where the system thinks you should be NOW. To change that, just win more to push where it thinks you should be, higher than it is now.