Changing how LP is gained and taken away.
Since initial rank placement is determined by the PLAYER'S personal performance in the placement matches, why doesn't LP work the same way. Imagine this, EX: you play Garen top against so-so and you end the game really well with a score as 12/5/5 with 200 so farm at 26 minutes, but your mid lane fed a Kat then she ended up carrying the other team to victory, you lose LP simply because you loss. Instead LP should be determined by player's role and performance of that role. In this I am considering things like actual end game stats as to the players performance while ALSO considering the outcome of the game. EX: you did really well in the game yet you lost, instead of losing 15-20 LP you could possibly gain 0-10 LP depending on how well you actually did. Another example is that if you don't do good but you don't do bad, you could not lose as much LP. Does it make sense that players should be held back by their teammates constantly forcing them to pray they don't get put with inadequate players. This also goes for the other end, why should bad players be able to piggy back on others to work their way through the ranks while others work hard to climb?
As for series and playing matches to determine if you rank up or not should have their own system entirely. While still utilizing my method to determine LP, the player will be presented a "goal" of a certain amount of LP to reach to level up. That way other people in those games wont be able to troll and sabotage their series, and it would be a better way to determine if the player deserves to rank up or not.
While all this would take it so many more variables in game play and algorithms to determine LP, I think it would truly be worth it to gives players a more fair and honest judgement of their ability.