I would look at school statistics or the common data set for each school. Just google the school and common data set.
For LMU, only 32% of enrolled students even submitted a test - so that shows you most didn’t which likely means they didn’t deem their scores worthy. The 25th percentile was 1260 and 75th percentile was 1410 - so it’s arguable as to whether you would even submit for admission. Some says if you’re below the midpoint - then don’t use it. Others say at the 25th percentile or below…it’s really a personal call.
This doesn’t answer your question but if it’s the highest level scholarship, I would assume those who get it would have a stronger score because LMU will have Ivy level or close to students - and a 1300 doesn’t get you close. Just an opinion - none of us know - but 1300, while very good, is not an elite score that the best scholarships might require.
Some schools - and they’re likely not in your interest set - but an Arizona or Miami of Ohio- look solely at GPA and have auto merit - Arizona a fixed amount and Miami a variable amount.
If you want to see how a GPA might impact a scholarship, there are auto merit schools such as Alabama - the top scholarship requires a 3.5 + 1420 and is worth $28,000. With a 1300, it’s $10,000.
At Alabama Huntsville, a 1300 would earn $13,275 whereas a $19,900 exists for a higher SAT with an UW GPA of 3.5 to 3.99.
Looking at mid size privates - these aren’t automatic
I did Bradley U - assumed you were from CA, had a 3.8 UW and I used a 1300 SAT and got $18K. Then I went to 1500 and got $20K.
Hofstra shows presidential at 1310+ getting $29K to $30.5K while at 1120+ getting $25.5K to $27.5K.
These are both mid size - so I imagine that yes, a higher score would be much more helpful (in general) - but for LMU specifically, if that’s the target, at least last year, less then a third even submitted a score.
Interesting, their (LMU’s website says “all” students will be considered) - I’d assume then that TO people can win - but have your child email their admissions counselor and ask to verify that if they go TO, they’d get full consideration for the Presidential - or have them ask what combo of GPA and test score is typically needed. They’ll likely get a vague response - but it’s worth asking.
PS - don’t forget, when they award these scholarships, they look at the entirety of the student.
What a scholarship really is - a discount - if you’re someone they really need on campus, they’re going to try to attract you to campus - via compensation - so the more competitive your son is as a person vs others, the better odds you have - but you won’t know until it happens.