Lyst is a directory service, collaborating with a variety of vendors, they do not handle any sales directly. Unfortunately, this results in a russian roulette like experience with zero CS or security.
I ordered five items from them. Four were great deals and the transactions were handled smoothly. For the fifth, I was fully charged and the item never materialized. It was impossible to obtain a refund (I made a purchase with a debit card so I could not contest the transaction through my bank). CS just led me around in circles for the better part of two months and they insist that I was never charged even after I sent multiple bank statements in, showing otherwise.
Be advised, Lyst is Russian Roulette. You may get a great deal or you may lose your time and money. Always shop with a credit card to at least have purchase protection because they will not really help you.