I just bought my own Tin Lizzie LS (used), and would hazard a guess that it's the encoders, especially since it happens only when moving horizontally. I know a lot of people have had encoder problems with the LS, and supposedly the DLS (latest Tin Lizzie) is supposed to resolve a lot of those problems -- but I can't afford to upgrade my machine right now.
My circuit board was bad on my machine, and I got a new one within a week; all is good now, so hopefully the new parts will fix your problems!