I could be very wrong, but I don't think that is correct.
Both the late "plain LGV" and early "LGV Spezial" abandoned the "Olympia" stock, for what Walther collectors refer to as the "UIT" one: a squared-up design with shallow parallel-sided fore end, mirroring Walther's rimfire match guns of the day. I believe what first differentiated LGV from LGVS was only the end-to-end springs, and a matte-finished barrel sleeve. The three bottom rifles in the left stack of frakor's amazing photo, moving up, are: early LGVS, late LGV, LGV Olympia.
Later Spezials had a thicker-walled receiver tube, milled scope grooves replacing the spot-welded ramp, re-worked trigger internals, and a deeper stock with sloped fore end bottom. The second-from-bottom rifle in the photo's right stack is one. The diffs between the LGV and Spezial, seem much less than between early and late Spezials...
Either way, Walthers are lovely but maddeningly confusing! Improvements came in an incremental - but never-ending - stream.