Yeah, Lamar University does provide scholarships based on merit. Here are some of them:

Cardinal Elite Scholarships
Total Worth: $32,000 over four years
Eligibility: $32,000 over four years
Minimum Criteria: a minimum SAT score of 1150-1290 (test taken Before March 5, 2016) / 1220-1350 (test taken After March 5, 2016) or an ACT score of 25 AND must be ranked in the Top 25%.
Separate application needed: Yes

Academic Excellence Scholarships
Total Worth: $24,000 over four years
Eligibility: $24,000 over four years
Minimum Criteria: a minimum SAT (CR+M) score of 1300 (test taken Before March 5, 2016) / 1360 (test taken After March 5, 2016) or an ACT score of 29 or greater
Separate application needed: Yes

Top Scholars Program: Mirabeau Scholarship
Total Worth: full scholarship for four years covering tuition, fees, room and board, and books
Eligibility: full scholarship for four years covering tuition, fees, room and board, and books
Minimum Criteria: a minimum SAT (CR + M) score of 1300 (test taken Before March 5, 2016) / 1360 (test taken After March 5, 2016) or an ACT score of 29
Separate application needed: Yes
Application deadline: January 1

Lamar University provides aids at an average of 5395 per student meeting 22% of students need. 95% of students with need receive financial aid at an average of 7776 need-based grant. They also provide other scholarships including Smith-Hutson Scholarship Program.