Riot doesn't share their system.
My best guess. As MMR is the core, MMR uses Ranges, The goal is to have MMR = The mean average of their good and bad standard performances. This is not inherently accurate, it has an adjustment period, and incase you ever improve, the ability to return to climbing at any point. Or sink if the opposite comes true.(not always player fault, buffs nerfs, reworks are things that can be negatives for a player.)
Now id make my Tiers and Divisions represent the entire ladder, and break it down by ranges, that way my Tiers actually have some meaning, they do represent skill well once MMR is accurate.
Then for LP gains I would make it off an accounts current MMR compared to their Range. Id use the range because its easy to generate as a value. Then would compare the players New rating after a game to that. If its to under that Reduced LP gains. If its above, accelerated gains. Balanced for being inside it or near the center of it.
How id approach it. No idea how viable or realistic that would be. Im still learning about the math still behind Elo systems.