LuckyModel's payment system is handled via a secure portal to their banking provider. Luckymodel themselves do not retain any of your credit card details. This means that your CC is charged for your order upfront before they actually ship, which may irk some customers, but on the upside, for this reason, if it becomes necessary for them to split a shipment, they do not hit you up for additional postage.
I have ordered from them many times over the past two years and have never had a problem.
EDIT: Be aware that the URL is www.luckymodel.com - if you inadvertantly put an "s" in there as you have in the thread title and in your post above, it will take you to somewhere where you may not want to go Not "work safe" and your partner (if you have one) may look at you with a raised eyebrow...