lychee
荔 refers specifically to the lychee fruit. It is a narrow botanical term with no broader conceptual center beyond the fruit itself.
荔 combines the plant radical 艹 with 劦, which likely contributes sound. The character was created to name the lychee plant.
The top grass radical 艹 shows it is a plant, and the bottom 劦 looks like three forces working together to produce a cluster of lychee fruits.
For レイ, imagine a lychee fruit wearing a tiny lei (Hawaiian garland): lei -> レイ, and the lychee is decorated with flowers.