A fresh lychee fruit easily beats its canned cousins in flavor, Refrigerate lychee wrapped in a dry paper towel, inside a perforated plastic bag or a container. “The lychee isn't a nut it's a fruit! What Do Lychees Taste Like? of them not as lychees but as a surprisingly complex tasting fruit in a can. Lychee fruits look like leathery strawberries on the outside, but on the inside The flavor of the lychee is like a combination of grapes and strawberries, and the Store lychees in the refrigerator in a plastic bag or container that is slightly open.