I can’t seem to find any information on it other than “ライチ” but I only found that from one website.:/
If you mean this fruit:
Then yes, it's normally called ライチ. It's popular in cocktails served at izakaya. It has kanji (茘枝), but this is not recognized by average Japanese speakers. Most people recognize this as ライチ, but according to Wikipedia, レイシ seems to be a more authentic name in botanical contexts.