I have never seen Fun Home on Broadway, but if we're getting a national tour, it will be for a proscenium stage. (I would think if we were getting an LA Company at the Taper, it would have been announced as part of the 2016 season)
My guess would be the Ahmanson. Next To Normal worked there, similar small show. If they close off the rear Mezz and rear Balc, the Ahmanson is nice sized theater and not barn like. (they won't close them off for a musical, but they could and they don't sell subscriber seats beyond the moving wall.)
Spelling Bee & War Horse both toured w/o a thrust stage and were great, so I won't write off the production even if it's staged differently.
I didn't know Love Never Dies was touring. That would most likely play the Pantages. I'll be first in line for tickets.