garyd, landshark - It's hard to know what the real current status is on the importation of limes and lemons at this time. I asked the agricultural inspector for documentation to justiy confiscating my limones, but he had none to give me. The restriction may not yet be covered by the USDA Import Guide, or, as woodspinner states, it may be an AZ state restriction. Federal BCI agents are required to enforce bordering state laws. On a recent trip south, I asked an agent at outgoing inspection about the importation status of limones, and he told me that there is a restriction on all citrus.
If you do an Internet search, there is info about some organism from China that is causing a problem. How it relates to limones from Mexico is unclear.
Citrus is susceptible to certain diseases that pose a domestic economic threat. However, certain diseases are environmentally specific. For example, the quick decline virus affects citrus orchards in California, but does not affect citrus grown in the desert environment of Arizona.
My neighbor in Penasco had a guava tree, susceptible to infection by a certain fruit fly. I spoke to a Mexican agriculture inspector when he came to check the insect trap in the tree. He told me that the fruit fly was not present in the desert environment of Penasco.