Does this slipper have a lip at the heel? Trying to reorder what I currently own.

There is no lip at the heel. It is a true open back slipper.

Can this gift be gift wrapped?

The official Amazon website says this about gift wrapping, "Amazon offers gift wrap on most items fulfilled by Amazon and from selected Amazon merchants. Gift wrap includes: 1. Gift wrap, box or bag appropriate for the item 2. Decorative ribbon 3. Printed card with your gift message on the top of the package The price of the gift wrap will be displayed with the gift details after you have entered the shipping address. Prices vary depending on the size and shape of the item you have purchased. Some items cannot be gift wrapped because of their large size, awkward shape, or because they're too fragile--these items will often be shipped in their original box rather than an Amazon.com box. If this is the case, you'll see a notice during the check out process that indicates the item will be shipped in the manufacturer's original packaging. You may mark "Ship in Amazon box" on the checkout page if you don't wish to reveal the contents (if available). If that option is selected the item will be shipped in an Amazon.com box at no additional cost." Hope this information helps & let us know if you have any more questions! Thanks for surfing with us, Your friends at ShoeSurfing.com