Simple, who do you think or who do you want the band to tour with next on the upcoming album cycle? Since there has been some criticism on their live show these last few years, who should the band pair with that would make you buy a ticket instantly? I would love to see them double headline with Muse, but I feel like that would have been better suited back in 2010/2011. It will probably never happen, anyway.
I would like to see Pvris/Chvrches/Purity Ring/Fallout Boy tour with them. Any or all of these would be great.
Probably depends on what their next album sounds like. My vote would always be Young The Giant as an opener, because they're easily my second favorite band. Muse would be awesome too, but for some reason it doesn't seem very fitting.
Any of Dropkick Murphys, Yelawolf, Wiz Khalifa, Enter Shikari or Halestorm would make me happy. Especially Halestorm. Oh yeah.
It'd be great if they toured with M83. But I know bands are weird about associating themselves with LP because of how they're perceived in the music world (not cool enough, not critically acclaimed).
With the worldwide comeback tour inevitable, I would have to say Thrice. Though I feel like that's a super long shot. A Rise Against tour that lasts more than 5 shows would be great though!