BYU could easily add lacrosse as a sanctioned sport and another women’s sport.
There are, as you point out few P4 schools that have teams. Lacrosse is sanction at Ivy League schools and service academies.
P4 schools (men)
Maryland
Michigan
Notre Dame
Ohio State
Rutgers
Syracuse
UNC
UMass
Utah
UVA
There are 28 sanctioned women’s squad at P4 schools, with Florida State set to add a team.