We reviewed a book a few weeks ago called Don't Throw It, Grow It (Storey, 2008) by Deborah Peterson. The entry for lychee (also spelled litchi) [p. 134], gives growing the fruit a rating of "easy," citing one person's experience of growing a lychee tree indoors to the height of 6 feet in about three years. You'll definitely need bright light.
Here's how Peterson says to grow Litchi (her choice of spelling):
Dried and canned litchi nuts can be bought every day of the year in Chinese groceries but these will not grow. You need to find fresh litchi nuts. To start the seeds, first remove the skin and eat the delicious pulp. Plant the seed in a moistened peat pellet withing five days of taking it from the fruit. The seeds should sprout in about two weeks.
Allow the seedlings to grow in the pellets until root fill the pellet bottoms. At this point, transplant each pellet to a 4-inch flower pot. Fill one-third of each pot with moist potting soil. Place the pellet on the soil, fill in around it, and barely cover it with soil. Place the pots in a bright window.
Has anyone grown a lychee tree from seed?
• Buy Don't Throw It, Grow It: 68 Windowsill Plants from Kitchen Scraps by Deborah Peterson, $10.95