Are LP gains capped?

Solution 1:

I earned 50 LP maximum. I was in Plat1 while my MMR was around Dia2 players. I skipped 5->3, 3->1 every time. I do not think there is a cap in LP gains, but getting high numbers are really rare, they only usually happen when a player doesn't play for a couple of months resulting in league drops. I have friends that gained about 70.

I do not totally agree but, here is an interesting post:

The cap is technically 100. It is rare, but some people skip divisions when their hidden MMR is much higher than their current placement. Therefore, skipping one division on your finishing promo game would net you 100 LP, and skipping multiple divisions would increase your LP gain by multiple hundreds.
So, say a challenger player makes a new account, and purposefully loses to get the account started in bronze 5. Each time he enters a promo series, he dodges games to drop back down into bronze 5, but his MMR doesn't suffer. The player continues to do so until he has an MMR of >3k. The player than wins his promo series, and is directly promoted to challenger. The increase to bronze 4 is +0LP, so that is negated. To bronze 3 is 100, bronze 2 is 200, 1 is 300, and the pattern continues.
The total increase would be a 2400 LP gain. I suppose this could be called the maximum.

http://forums.na.leagueoflegends.com/board/showthread.php?t=3947302