Probably like Resogun. Automatically slowed down to 30fps. But I can feel slightly lag compared to the PS4 version.
Does Resogun slow down (when viewing it on the TV screen)? I was under the impression that the remote-play feature is tied into the gameplay video feature (or vice-versa) and that all the PS4 does, is continuously record a video stream at 30fps. If you have remote-play enabled, that stream that can also be used to save as a video is transmitted/streamed to the screen on your Vita on the fly. You are, therefore, effectively playing a video stream that is recorded at 30fps while the Vita sends the controller mapping that controls the game on the PS4. I'd be quiet surprised if there is any logic that a game-dev has to take into mind for remote play since it's practically enabled by default, regardless if there's a Vita connected to it or not. I'm also not sure you would have more lag - just more noticable because the game actually runs at the double the speed and you're not seeing the updates as frequent enough as the game developer intended...
IMO, you shouldn't have more lag if the game runs at 30 or 60 - it's just more noticable in one instance because you're playing it on a 30fps feed.