Tuition Exemption Scholarships for Nonresidents:
1360 SAT/ 31 ACT and a 3.8 GPA who submit all required application materials by November 15 of their senior year are automatically eligible to receive this award. Students with excellent test scores and academic grade point average are eligible for consideration.
I am from Texas as well, this is what I had, but not sure if it is still offered. Saved me over $60k, still had to pay the fee's every semester, but that was never more than $1,000-$1,500.
Best advice to you and your son, is to take an SAT/ACT prep course (I preferred SAT, although I think the test has changed since, but LSU will convert either to the other), they are totally worth it. They won't make him magically smarter, but it really helps to familiarize one with the test, and from what I remember, that's all LSU cared about. i.e. I came down to visit, did not have high enough scores, took a test prep, sent over new score, and turned about $1k into $60k. Now, I could be giving the test prep too much credit, but I still think it was one of the best investments I have ever made. (my parents made me pay for 1/2 of it so I wouldn't blow it off)