Instead of spending on getting an engine swap, wouldn't it be more economical to buy an LR4, with a beige interior, in great condition and get it painted or wrapped? Getting an engine or transmission swapped would require you to source a donor unit and pay someone to do the labor of swapping them. That is NOT going to be cheap
That said, if your search is specifically a 2016 LUX, that already will narrow your search immensely. Open it up to 2014-2016 (post facelift and with the SCV6) and/or give up on the LUX (which is probably the tougher ask) your options will expand quite a bit. That color wasn't sold for very long as a 2016 model I don't think. They started selling the Landmark edition and the only brown is Zanzibar.