Brian, I see that you have some beautiful citrus in your greenhouse as well as some more tender tropicals. This is a good sign that you will be able to keep lychee alive in my opinion. I think the biggest challenge that you will have is polination. Lychee needs insect polination, so if your tree blooms at a time or in a place where there are no insects to pollinate the flowers, I think your chances of getting fruit are slim. Also, from my observations, pollen is not as viable in cold weather (this may be variety specific as well). Maybe you could keep the tree dormant by withholding water until later in your spring.