Electronic gift card, you are absolutely right, as that's processed by Cashstar, not Lululemon, and will surely not trigger things on the Amex side, which clearly start from the vendor ID on the charge.

But the physical cards which are bought from and ship from Lululemon? Not sure why that would be different than one bought in store. It's clear that Amex either doesn't collect purchase level data, or doesn't care to parse it out, with regards to Saks and airline credits, so I think for now it's a reasonable assumption that this will stay the same on this one. Could be wrong, though of course!