Awesome tree, is that yours? I forget where I read it and what fruit it was specifically referring to but I've heard that lack of Calcium and inconsistent watering may cause cracking. Ideally, your tree will have roots that go deep into the soil where moisture levels are more consistent. I find myself often watering my trees, perhaps too often, and encouraging shallow roots. I know most Lychees are from air layers but I have dug up several air layers I planted and they do send roots deep down into the soil.
I'm sure desert conditions such as dry winds can also be the cause of the cracking. When I went to my dad's Lychee Lychee grove in China, it was relatively humid and not windy.
Simon