That's a good question that I'm probably not qualified to answer. I might have been a bit careless in using the term "traditional". What I think about when using the term in connection with Lapsang Souchong, is the smoke-drying over pinewood (and not pine tar, as with "tarry lapsang"). Whether or not there are other parts of the processing that are relevant as to whether a lapsang qualifies as "traditional" or not I don't really know.
There's a "Traditional Lapsang Souchong" for sale at a very affordable price at YS, and while it's a decent daily drinker it's nowhere near the quality of the mentioned sample offered by CWS, or the lapsang sold by Jing Tea Shop. I don't think the quality of the leaf is the only difference between these teas. I have a hunch that the processing is quite different, but I don't really know.