Pruning a lime tree's roots.

It doesn't matter what species of tree that is container bound eventually the root mass will get too large and require some maintenance. Some species grow very fast and others will use the nutrients and the soil will collapse before the roots overtake the space offered them. This is a Persian Lime and to keep the feeder roots in the correct orientation and the tree vigorous and healthy I prune the roots in the early spring.
I jokingly call this 'big bonsai' techniques but it really is very similar how bonsai trees are kept in the small shallow planters. The key to keeping any tree in a container is root health. If the roots are happy and doing well the rest of the tree will be proportionately healthy.