The photos you have provided are consistent with mockingbird pecking and scratching.  In home landscapes, mockingbirds will frequently visit citrus trees and peck the fruit.  The damaged areas that appear to be growing on your fruit are focal areas where they have returned to peck the fruit again and again.
Usually this damage is confined to the peel--we think because these birds are using the citrus oil for some purpose such as preening feathers or insect resistance.
In drought conditions they may peck through the peel to get to the juice.
Bird netting is suggested to eliminate this problem. Other bird scaring devices may help in some locations.

Thanks for the answer.  All the lemons are pretty much "goners" this season, so I might as well run an experiment.  Generally, I entice birds away from crops by offering something even yummier as a distraction.  If I have citrus-peel eaters, I will experiment by putting a feeder tray loaded with citrus peels near the tree.  If they are after the peel only, I can provide the peels on a more stable feeding platform (compared to the spindly lemon branches).  If they prefer the easily-accessible feeder peels, then I need not have the unsightly netting.  (A similar tactic with bird feeders kept my tomatoes "unpecked" for years.)  Perhaps that and some bright pinwheels in the citrus pots...