Hello, DeniseM. How did you start your tree? seed
? Cutting? From a nursery?
A lot of citrus have thorns. My meyers lemon does not but my kumquat does. Most grapefruit do have thorns as well. I have never grown a key lime but it may be one of the thorny ones.
If you purchased a grafted tree from a nursery, then it will be probably normal for that tree. But if you began it from seed
or a cutting, it may be another type of citrus altogether and may never fruit. Although you can be surprised.