Only prune the tree as needed to keep in bounds, and to keep shapely, and small enough to keep portable and warm.
Root pruning will be necessary if you keep the plant in the same pot for an extended period (2yrs or more approx)
I have a large lychee in a 25 gal, and its only been in the pot for about 1yr, and it will be root bound by the end of this year for sure...
I will have to root prune and repot in a larger pot, or repot in the same pot.
I always prune leaves and branches somewhat, if I prune roots (it helps the tree heal faster)
Another trick I'll share with you dudes, is the practice of setting a plant in a pot at a low depth (not high up in the pot like Zill sells trees, no offense to Zill...he is short term container grower and has high turnover rate for plants) But if you plant a specimen a bit low in the pot, you can step the plant up in the same pot, over 4 or 5 times!
It saves money, and plastic, and water seems to fill the pot, sitting on the roots and the plant doesn't have fertilizer or soil being splashed out over the rim when heavily watered