In my experience, the free shipping is not actually free because lately it has always excluded LV-only purchases. Plus, free shipping is only when eLux is running a promotion.
I think there used to be free shipping promotions on eLux that included all purchases, but lately, as confirmed by a CS rep a few months ago on one of my orders, the policy has changed to exclude orders containing only LV items.
A way around it is to buy a non-LV item in addition to your LV item in order to meet the terms of their typical free shipping promotion. Depending on what you're buying, though, that might or might not actually save you any money.