Transplanting it into the ground will disturb its roots because you want to straighten out any circling roots. When you disturb the roots, you can trigger fruit drop. Lychee naturally has several rounds of fruit drop as the season progresses. Because your tree is so small, I would plant it now at the risk of losing fruit.
Young trees often don’t set fruit and even if it did set fruit, it probably won’t be ripe until around August or September. This means you won’t be planting your tree till around Fall and it would have lost all that time that the tree could have spread out it’s roots into the soil.
You could get luck and transplant your tree into the ground and your tree may still set fruit so I would definitely plant your tree in the ground now.
Simon