to answer your question simply, Yes, you can.

some people do, actually pruning their trees to about 4 foot every year. the next years fruit all come on new growth. they prune this time of year after harvesting fruit and the trees normally go dormant around November.
visit Going Bananas, Don and Katie grow acres of Mauritius this way and will be happy to show you first hand everything they do.

some people like Harry like to let their lychee trees grow. most grow to be large upright trees, some cultivars are smaller. lychee limbs are prone to wind breakage.

Thanks mango kush.......I saw an old post of yours about Don and Katie and how they do a hard prune every year. I'll have to make the trip down there and see their operation, sounds like they have a good system for our climate.

Thanks again for the help!

Johnna

Jonathan Crane makes some excellent videos on pruning and mulching lychee trees

Here is a link that might be useful: youtube