Close. Actually the parabola part didn't play a part. What actually occurred is that, when you're dashing to another unit (for reasons I cannot fathom) you arrive at a random short distance from them. If you started your dash at a closer distance than that random short distance, but not exactly on top of them, some funny math happens.
In order to smooth the arrival (again, for reasons that I cannot fathom), the two distances are divided by each other to come up with a speed scaling factor. Unfortunately, that can lead to dividing a larger number by a smaller number. Sometimes a much smaller number. So for a single frame of simulation, Lee (or Irelia, Jax, Yuumi, etc.) could report that they're going hyperspeed. Like cross Summoner's Rift in a tenth of a second fast.
Then, in the area trigger/missile collision, we ask "hey, where were you last frame" so we can do "capsule collision" (pretty standard game collision technique). In order to compute that, Lee says, "Well, I'm going super ridiculously fast, so apparently I was waaaaaaay the f*ck over there."
The fix was to take the min of the scaling factor (from dividing the distances) and 1, to make sure that we're not blowing our speed way out of proportion.