Should the thorny branches be trimmed out of tree?
Almost all citrus will have thorns at some point in their lives. Now this comes with a few more questions. Does the majority of your tree have little to no thorns? If this is the case, and there is a branch with more than usual, then this could be coming from beneath the graft point. If this is the case then you can prune the "suckers" out as needed. If this is from seed, then I would expect to see thorns all the way until they are old enough to start bearing fruit. If this is just a branch that is in the way of the rest of the tree then you can cut it out at almost any time. It is best to do so when the tree is not flowering.
Here is a collection of citrus articles to help you start identifying citrus and their issues: https://www.gardeningknowhow.com/edible/fruits/citrus/