I got a 171 (99th% when I took the test, the same as a 173 today) without knowing anything about the test and not doing any study specific to the test. So, for me it took 0 study hours to get over a 170.
I also taught for two national LSAT test companies. In an 80 hour course, for the students that showed up and did most of the homework, 7-10 point improvements were common, (at least while I was teaching). Since there is about 2 hours of homework per hour of class time this equates to 10 points per 240 hours of study. This is just about where another poster gave some formula which basically said 30 hours per point.
Where I disagree with most other posters is on the ceiling. I know the LSAT is a skills test, not an intelligence test. Let's compare another purely cerebral activity, chess. Early on in IQ research they tested the IQ's for the top ten chess players in the world and, surprisingly, found they had average IQ's. Other research has discovered what distinguishes them from the rest of us; the top level, internationally rated players put in an average of over 29,000 hours of practice. The next highest level of internationally rated players had put in over 19,000 hours. This means, in chess, at the highest levels, moving up in the rankings basically requires 10,000 hours of dedicated quality practice.
So, although the law of diminishing marginal returns probably applies to LSAT study once you gain your first 10 points or so, there is probably no ceiling on your potential score. It becomes a practical issue. I have heard of very few students who put in hours in excess of 300 or so hours. Compared to the 4,500 hours class and study for undergraduate and the 4,500 hours for class and study for law school, most students really put in very little time studying for the LSAT.
My working hypothesis is thus: A student who scores a 145 on a practice test and works with a highly qualified tutor for 400 hours and purchases quality books and materials who works 8 hours per day on LSAT study for a full year, thus putting in 2,000 hours can break a 170.
This requires being unemployed for a year and spending $25,000 to $50,000 on tutoring but probably has a positive economic return. The reason student's rarely do this is because the $100,000 for college and the $100,000 for law school can be financed, but the living expenses and tutoring for a high LSAT generally must be paid up front.