While I don’t know much about Law School, but I find it very hard that the LSAT score can be such an important factor in admissions. Usually schools (at least undergarduate) look for many other things besides SAT scores. They want extracurricular activities, scientific research, athletics, music, volunteering, social awareness, good essays, top recommendations, etc. etc. etc.
If Harvard wanted, they could set their minimum score at 800 on all sections of the SAT, and still not have enough places for all qualified applicants! Since they have a range (usually in the 700’s) obviously they are using other criteria which they weight more heavily than the SAT alone.