Yes, either that or maybe Tim Palmer. He has produced the Julien-K debut album and the sound is just badass, but of course I have no clue if he could work with a band like LP which sounds totally different from Julien-K.
Or why not go for Don Gilmore again? I loved the sound of the first two albums, and he might also be a great match for the sound of the upcoming album.
But yeah, Mike producing it himself would be the best solution, I guess.