On our lime tree each lime, as it grows full, starts forming a stump. It looks like a miniature version of a tree stump on a lime. I haven't done too much research yet, but being online in this site I wondered if you have a possible clue/know how or what it is/might be and how to treat if it is a health hazard.
I have not found any information on a disease of lime trees that has the issue you describe.
If you wanted to send an image it could help with identifying the problem.
Here are some links for you.