In all honesty, I have NO IDEA what these bands/promoters get up to. That said, with the relatively heavy promotion of Lightning Bolt I would be shocked if they didn't do a relatively thorough tour of Europe - which would include at least one gig Italy, if not two.
It seems the band tends to take advantage of the festival circuit as much as possible these days - especially overseas. They aren't playing any of their own gigs in Australia and NZ. I can't help wonder if they'll do (mostly) the same in Europe.
Only Germany, Netherlands, and UK (and Ireland, I guess) seem to be getting their own PJ shows these days.