Yes, schools go give merit scholarships to "old" students.
I am also "old" (50). I took a practice LSAT last summer with no preparation and got in the mid 150's like you. Then I studied about 150 hours all summer and part of the fall, and got 178 (99% percentile) on the real test on September 29. First I studied a prep book from Princeton, I think. Then I studied the "Bibles" and many, many old actual tests. You can buy these on Amazon. For me, the hardest part was the games. So I actually wound up doing each real game section at least three times, spaced out a few weeks apart usually. It was like an extra job or a hobby that bordered on obsession. If I had not taken it so seriously, I would never have scored so high. I probably spent around $1,000 on preparation, the test itself, a motel room near the test site the night before etc.
My undergraduate GPA was 3.4, not high at all these days.
Then when scores were reported, I started getting emails from all sorts of schools inviting me to apply without paying their application fee, so I applied to around 18 or 20 schools, just for fun. I received many partial or full tuition scholarships based on merit, from schools all around the country, even some T1's.