I have this very healthy producing tree. This season I started noticing that some of the lemons closest to the trunk are completely & perfectly peeled off - no skin left just the fruit. It is like when one peels an orange for the kids.
I could be squirrels but I don't think they could and would and peel it perfectly without disterbing the fruit the members at this forum www.citrus.forumup.org can probably help you more with your problem.
Goldelina, do you see the skins on the ground or are these lemons possibly forming without skin?
Since you mention that some of the lemons closest to the trunk are doing this, I'm wondering if it could be a genetic mutation.
Another possibility could be your tree is a "Chimera: A plant consisting of two or more genetically distinct tissues or an artificially produced plant having tissues of several species."
Here's a picture of katydid damage to the peel.
https://edis.ifas.ufl.edu/EDISImagePage?imageID=1097544773&dlNumber=HS122&tag=FIGURE%2030&credits=