As it turns out, all these spellings are already accepted, TRex, apart from the one in your heading,
litchee.
Litchee is given as an alternate form by the vocabulary.com dictionary and by Wiktionary. An example of a publication which uses that spelling is
Rawsome!, a 2004 book by Brigitte Mars, subtitled
Maximizing Health, Energy, and Culinary Delight With the Raw Foods Diet. At the time of writing, Amazon ranks the book 342 in the Raw Cooking category:
Litchee (also spelled lychee or lichi) is a sweet fruit just a bit smaller than a walnut, with a flavor reminiscent of grapes and an aroma like a rose. Fresh litchee fruits have a cool energy, but when dried, they are called litchee nuts and have a warm energy.
Litchee will be accepted from now on.