Both teams are very competitive but lacrosse in particular is a sport in which the current head coach actually cut a significant number of recruited players coming from NAPs in his first year. He also speaks in favor of a smaller roster and has a big recruiting class coming in. There's an excellent club lacrosse program, though (which does sometimes have cuts too).
Sprint football also recruits but at least from what I've observed the chances of making it as a walk-on may be better.
Maybe your son was recruited in one or both of these sports, in which case this probably isn't relevant to you, but I read your post as suggesting your son wants to walk on. If he does decide to try to walk on in a sport, I'd advise trying to contact the coaches and give them some info on his skills/accomplishments before-hand if possible so he's not just a number on the mandated open tryout day.
