It always annoys me when Green Day close with Good Riddance, it's such a downer. They need to have Minority as closer, that song kicks the crowd into overdrive!
As for LP, no I don't think Messenger should be a closer... but then I don't think Bleed it Out should close either
For me, the closer should be One Step Closer or In the End- like it or not, that song always gets the biggest reaction at shows.