LP is called League Points. You get League points for when you play Ranked games. You also Lose LP when you play ranked if you lose. LP is given and lost based solely on whether you win or lose and NOT individual performance (big mistake in my opinion). The amount of LP you get is based on how long you can push the match out. So if you play a 45 minute game you would get more than if you were to win at 20 and if you win by FF@20 or just by FF alone, you get less LP than if you were to destroy the nexus.
The amount of LP you lose works on the same thing. If you play the whole match with no FF then you lose less LP than if you were to FF.
But again, it is given and taken purely on whether or not you lose.