Will
Re your comment about the 3nm displacement.
LS is, I think, not referring to the actual a/c position but to the relationship between a "straight line" on a chart, over a short distance, and the actual shortest distance (i.e. derived from a great circle or the distance as per spherical geometry). The shorter the distance the less lateral deviation between the two. The greater the distance, the greater the lateral deviation.
So it seems you are both saying the same thing: A 3nm lateral displacement over that distance (119 nm) is much more than can be accounted for by citing the differences between navigating and/or plotting positions using a straight line on a chart, or a formula that allows for navigating over a sphere (as per WGS84, GPS software, etc).