Unlike many fruits, lychees do not continue to ripen after they're picked, which means it's important to time your harvest as well as possible. ... Lychees that are ready for picking are sweet, but with a slightly acidic flavor.
How do you ripen lychees?
Wrap lychees in a paper towel and store in a perforated plastic bag. Lychees produce very little ethylene. Keep humidity level high and the temperature at 34 - 40ºF.
How do you know when a lychee is ripe?
To check for ripeness, gently press on the skin with your thumb. It should give a little. If it's too soft, it may be overripe.