Yes, it’s likely they’ll have to win it. The lax tournament committee has always leaned heavily on RPI – and the LU RPI rank is #17. Likely slightly worse if they lose in PL tournament. Probably would need to be #13 or better to have a shot.
To have an at-large shot, LU would need a few of these things to happen:
1. Johns Hopkins loses to Loyola (or Army)
2. Princeton loses to Cornell in final regular season game – and does not win the Ivy tournament.
3. Cornell wins Ivy tournament.
4. Albany wins America East tournament.
5. PSU wins CAA tournament.
6. Ohio State loses to Fairfield and/or in first round of ECAC tournament.
7. Syracuse loses to Notre Dame and then loses in first round of Big East tournament. (And Notre Dame wins Big East tournament.)