As others have said, my first thought was the SUNYs.
You’re looking for DIII lacrosse, but at a school that isn’t too small, and for 30K/year or less, with stats/rigor that will not pull in big merit from competitive schools… and also colder weather. Those are a lot of constraints.
The mid-sized SUNY schools have solid STEM, DIII Lax, and both flagship-match and merit to get you within budget. Also, the travel isn’t onerous, because the whole league is composed of SUNY schools: 2022 Men's Lacrosse Standings - SUNYAC For an athlete in a demanding major, keeping the travel manageable can make a real difference.
I’m not familiar with whether the playing level at DIII vs. DII schools overlaps - would DII be a possibility? A strong STEM school with an NCAA DII team is U of Alabama Huntsville (which has a cooler climate than most of Alabama). Auto-merit would bring UAH within budget, with his GPA, if he can clear a 32 ACT or 1450 SAT. (If his weighted GPA hits 4.0, then the test-score threshold to make budget drops to 28/1310.)
Would a club team work? U of Maine’s club team plays in MCLA DII, and that’s another flagship-match school where you’d pay, at most, the in-state cost of UConn. SCSU is also in this league, as is URI, although I’m not sure whether URI could make budget or not. UConn has a D1 club team (as does UNH). I’m not knowledgeable, at all, about how club team playing levels compare.
In terms of privates that are large enough and might give enough merit… maybe Ithaca College? (4600 undergrads, and cross-reg potential with Cornell… and they have a business minor that could complement the CS major.)