I had the same leaf tip browning on my lychee for about 3 years after I planted it. Sometimes half of every leaf would turn brown. I dug compost in the bed a couple of years ago. The big improvement though coincided with when I began a daily soaking, filling a 4" deep trench around the tree with water. More new leaf flushes appeared after a couple of years of almost no growth and the new leaves are staying green. Still hasn't fruited.
i had the same thing also with one in a container.
seems there was little organic matter left, the soil had become hydrophobic
it needed daily watering.once i put it in ground it was resolved.
My other lychee had tip burning and simple mulching fixed it.
im a big believer in mulch for anything in ground.
it keeps soil moisture stable, and rain from tearing up the soil.