beachlady, I fear there are few choices in Kansas itself...the Kansas State activities association, which oversees the "officially" sanctioned sports, does not include lacrosse (
Activities sponsored by the KSHSAA). Most likely the schools mathguy found

sponsor lacrosse on a "club" basis...that may not mean they don't fund them well and the competition is keen, but check that out first, don't just assume it will be like "varsity"
also, some of the schools are in the St. Louis area as well as the Missouri side of the KC metro area...they are all in affluent suburbs or expensive private schools...the schools actually in Kansas (near Kansas City MO) are:
olathe, shawnee mission, and blue valley north (all public)
the schools in the KC Missouri side of the border are:
aquinas, (if the one I'm thinking of), rockhurst, pembroke, and parkway (only the last is public)
the others are in the St. Louis area or at least the non-KC area...
Search carefully--if your son is a strong player, he could be a star--but assume that with so few schools , that most teams are pretty good, because a small number of schools share the pool of players.
Kansas is not imaginative in sports beyond the big three...most high school athletic directors still hate soccer (they fear it diminishes the precious football team). The KHSAA does sanction bowling, though!
325 H Webster Groves ( 8- 8, 79.7) 7- 8
331 H St Thomas Aquinas ( 3- 8, 74.9) 12- 2
402 A Chaminade Marianist ( 1-10, 74.5) 5- 1
402 A Hazelwood Central (11- 4, 84.5) 8 10-11
407 A Rockhurst Jesuit (13- 4, 93.6) 3 2-21
412 A Olathe ( 6- 6, 78.5) 9- 6
416 H Columbia Hickman ( 8- 3, 84.5) 7 6- 9
416 H Springfield-Glendale ( 3- 9, 74.9) 11- 7
417 H Ladue ( 6- 6, 79.9) 8- 5
428 A Pembroke Hill ( 8- 3, 82.6) 6- 7
430 H Parkway North ( 5- 9, 76.5) 16- 7
504 A Shawnee Mission ( 1-13, 73.0) 11- 3
510 A Blue Valley North ( 0-11, 70.0) 13- 0