Well, uhh. He gets to be a dick. That's #1 I think. But other than that, he gets to offload Sansa into one of the safest spots for him. The match bolsters Bolton's position in the North -- but LF is betting that it won't matter (and that Stannis won't kill Sansa in the process of ousting Bolton). It mollifies the Lannisters because it does bolster Bolton.
Sure, he could have given her directly to Stannis. But that would be unsubtle. If Stannis does lose because of reasons (it happened already), it would mean that LF has no escape plan -- he openly declared. This way no matter who wins the North, LF will be positioned to take advantage of it. Remember, he expects Sansa to be his insider in the north. He expects Stannis is just marching through on his way to Kings Landing. And afaik, LF's personal domain is right next door to Sansa.
Doing that with Sansa is hedging his bet and solidifying his personal political position, as well as serving the creepy ass "I'll make her into the woman that Kat never was and then marry her" vibe he's got going for him. That's what I get from it, at least.
About the worst thing that can happen for LF out of this is that Sansa gets moody and commits suicide. As long as Sansa lives, it's a matter of what and how much he wins rather than what he stands to lose.