If your tree is very large and not fruiting, aside from not enough chill hours, it could also be getting too much Nitrogen, even from organic sources. If you apply organic fertilizers, try something like 0-10-10. Having leaf nitrogen below a specific level, which I don’t currently recall, can tilt the balance more towards blooms instead of vegetative growth.
Lycheesonline.com has some great info on growing lychees and getting them to fruit. As Rob stated, you have to prune your trees at the appropriate time.
http://www.lycheesonline.com/HowToGetTreeToFruit.cfmTake a look at when your neighbors harvest their fruit and prune when they harvest their fruit or when you see them pruning, which should be right when they harvest their fruit.
Some geneticists and plant researches like Tracie Matsumoto have hypothesized that Lychees and Longan may have a flower inhibiting gene called “FLC” which is found in Arabidopsis. She also believes that there may be genes or environmental cues that can suppress the FLC gene in Lychees. For Longan, they have already found that firecracker ingredients can force Longan to flower and fruit out of season.
A long practiced technique that has proven effective for promoting flowering and fruiting in Lychees is to girdle a portion of the tree but this practice should only be attempted if you know what you are doing or you only girdle branches that you are not afraid of losing.
More info on encouraging Lychees to produce more predictable crops. I’ve had the pleasure of emailing Francis Zee about Lychees and he is very knowledgeable and passionate about Lychees.
https://agresearchmag.ars.usda.gov/2009/may/lycheeLychee production in Australia with lots of info
http://www.fao.org/3/ac684e/ac684e05.htmStrategy for Kaimana Lychee in Hawaii
https://hilo.hawaii.edu/panr/writing.php?id=254Simon