Before the tournament, all teams have the opportunity to submit bids to host regionals and super-regionals. Usually, this is something most teams do routinely even if they know there is little chance they will be seeded 1-16.
It does come into play if two unseeded teams win opposite regionals. In that case, the first criteria is whether one or both teams submitted a bid to host super-regionals.
I believe the second criteria is whether the teams involved were 2-seed, 3-seed, or 4-seed in the region they won. A 2-seed hosts over a winning 3-seed, etc.
If both teams are the same regional seed, as is most often the case when this happens, the team that won the regional at the highest seed hosts.
Since Washington is the 7-seed and LSU the 10-seed, Minnesota would have first opportunity to accept an invitation to host a super-regional between them and anyone from the LSU region except for LSU, provided they submitted a bid.
The NCAA will at some point start seeding 32 teams rather than the current 16, like they did with volleyball last year. Under that scenario, Louisiana would probably hold the upper hand, since they finished the season at RPI #11 and likely would have been seeded higher than Minnesota.