And, by the way, I read that some lemon trees can continue to bear fruit for up to 50 years, so I'm hoping there is still a little life left in yours!
I know that Florida had a bit of a cold snap earlier this year - was your lime tree like this before the cold snap?
Have you seen any evidence of insect pests? This article will assist you:
I can't exactly tell from the photo, but is only one main branch affected? The rest of the tree except for that one spot looks green unless the photo is deceiving me. If the branch is truly dead, you may want to consider removing it with a pruning saw, cutting as close to the trunk as possible. The best time to prune lime trees is early spring or late summer or anytime prior to blooming.
Have you changed how you care for the tree in terms of fertilization or watering? Double-check the care of your key lime tree by reviewing the information in the following article: