Certified GKH Gardening Expert
Pruning lemon trees isn’t generally required, but there are several good reasons to do so. Pruning helps improve airflow, reduces disease, strengthens limbs and makes it easier to harvest fruits. The best time to prune is early spring or late summer or anytime prior to blooming. Prune every year or two, which will help keep them from becoming too large. If you have frost damage, wait until the trees have shown new growth. Prior to pruning trees, pick off any remaining fruit. Prune all dead, damaged, weak or diseased branches to the base. Weak stems cannot withstand the weight of heavy fruit production.
Lemon and lime trees are quite similar, including their care. Pruning lemon trees isn't any different than pruning limes. The following article should be of some help: https://www.gardeningknowhow.com/edible/fruits/lime/tips-for-pruning-lime-tree.htm