Without that bid, the NCAA is free to match up two ACC teams in the first round of the tournament. For the most part, that puts Duke, North Carolina and Virginia as the most likely schools to get matched up against each other in the first round, since the first round is largely geographically based. However, it's also certainly possible that Duke or North Carolina could face ND in the first round, if both of the schools in question were looking at an air travel game in any event.
Regardless of eventual conference alignment, I would expect that Utah will try to schedule both Denver and Air Force annually. While neither is close enough for a bus travel game, they at least eliminate the possibility of jet lag with these two teams on the schedule. Utah will be only the fourth or fifth Division I men's lacrosse program outside the eastern time zone (Air Force and Denver are in the mountain time zone, Marquette and perhaps Bellarmine are in the central time zone.)
As for Pac-12 schools, in addition to USC and Stanford I've also heard Arizona, Arizona State and Colorado mentioned as potential men's lacrosse additions. And while I haven't heard them mentioned, Oregon has a decent amount of in-state talent available, not to mention seemingly endless funds from Nike. Of course, Title IX is a potential issue for any of these schools, and I don't know where any of them stand on that. But I think we'll see the Pac-12 add men's lacrosse in the relatively near future, perhaps with affiliate members. Air Force and Denver make the most sense in that regard, and perhaps Texas is a possibility should they add men's lacrosse.