Three hours would certainly be a disaster the way LP does shows currently. I think, with the tour schedule that LP seems to be doing now, two hours could be doable, and could leave the fans going home happy.
the band being popular has nothing to do with it. most of the discussion concerning LP's live durations are that Chester needs to use his voice but not overstretch it, to play for about 3 hours each night would kill his voice.
venues are strict about timing - every venue has curfews which bands must to adhere to or they get fined for over-running and violating noise laws.
also I don't think you can compare LP to Foo Fighters, or any other band for that matter. Foo Fighters/Green Day etc. bands that play these real long sets each night are entirely different to LP.
relative popularity has nothing to do with set duration, it's dependant upon each individual band. LP choose not to play these long sets.
And quite frankly, I don't think they could pull that off - their stage presence isn't massive, they play the songs and don't make a much of an effort to interact with the audience and put on a show per se. I'm not dissing the band, that's just their style, i think nything over the 1 & 1/2 hours they already play is long enough, three hours of that would get really dull.
Two 90-minute sets could work for the HC tour, maybe if the tickets weren't 100 dollars.