Let me tell you why half LP gains shouldn't exist during loss prevented
First, a history lesson. When Riot first started doing loss prevented it was similar to what it is now: half LP (elo at the time) gain per win, no penalty for a loss. However, the difference then was that you could continue to queue for ranked even while loss prevented was disabled. Some people used this opportunity for free shots at elo and at the time it makes complete sense for there to be half LP per win. This is of course no longer the case, as Riot disables ranked queues upon activating loss prevented. Now that the largest potential abuse case is out of the way, let me tell you why LP gains should be at full during loss prevented.
It's very very frustrating to win a game that had minimal issues but lose half the points last second because loss prevented was turned on. It's even worse when potential lag favored the enemy team over your own (a spike occurs during a tower dive, a teammate disconnects while they maintain a full team, etc) and you try your damnedest to overcome it, only to be met with half gain. With diamond 1 clamp and earning a +2 or +1 off a hard fought game is one of the worst feelings league [the system, not even the players] can provide; I might as well have gotten drophacked. On the other side of the coin, in all my post-games with loss prevented, the losing team has not once been spiteful and said something like "haha you only got half gain". All they care about is that they didn't lose any LP, which leads me to believe that no one will cry for "unfair gain" should someone gain full points off winning a laggy game.
Also, in the rare situations the team finds out it's loss forgiven via a friend or something, I've had my team immediately start troll building or in the most extreme case immediately FF an otherwise even game. And can I really blame them? When a game comes between +2 and +0 the incentive to continue is really not there.
And to conclude I present this http://gyazo.com/173ca9bc46276d92be314d5d26c8c1a7. July 29 was a terrible day to play league of legends. Feelsbadman.jpg