Just for background to some of this discussion...
The usual number cited is either 6 or 7 at more or less any school that ever mentions caring about the average, the idea being that if your score band is +3/-3, then you're performing differently if you're 6-7 points higher on the second test. (LSAC says that people, statistically, will vary between 3 points above and 3 points below a given score upon repeated testing without significant changes in between [e.g. studying] That score is called your "true score," and it is thought to be the [theoretical] accurate measure of your ability to take the LSAT. The +3/-3 is the score band.]
To illustrate the point, let's look at an example. Let's say you get a 165 on your first test. That means that your "true score" could be anywhere from 162 to 168, based on LSAC's score band.
Let's imagine that you jump 4 points on your second test. If your next score is 169, with a score band of 166-172, then they figure that 166-168 (the overlap of the two score bands) is probably your true score, so they average your 165 and your 169 and get a 167; this 167 is probably a good estimate of your "true score" (or so they think).
On the other hand, let's imagine that you jump 10 points. If your second score is a 175, suggesting a score band of 172-178, they don't know what to do. A score band of 162-168 has no overlap with 172-178, so one of those scores was more likely an anomaly.
That's the reason for the margin of 6-7 points. If you jump 6 points to a 171, your band is 168-174; there's an outside chance that your "true score" is a 168, but you would've had to be very unlucky on the first test (-3) and very lucky on the second (+3). If you jump 7 points to a 172, the score bands have no overlap at all, and now you're in anomaly territory.
So there are quite a lot of schools that want you to write an addendum if your score jumps 6-7 points or more on a retake. Your goal in such an addendum is to talk them into thinking that the anomaly was the first score, not the second.