Riot punished me for winning a 4v5

I was in duo queue with my friend. We found a game and started, but after about 10 minutes our top laner decided he was done for the day and left the game. Fortunately we hung in there and continued to fight to win, and after 40 minutes we managed to win the game. We were really happy about it until we saw that for some reaon we only got 15 LP. Can someone explain to me why I only got 15 LP for winning a 4v5 against players who all were higher ranked than me?