Former barkeeper here: usually the limes and lemons are bought as-is-available, which usually means mass-produced stuff laced with pesticides. Organic fruits are, due to their higher price, normally only available in hipster places.

The rind is not considered edible in any way, and the pesticides don't migrate through the rind. Which is, btw, a good reason to rinse any fruit or vegetable (prior to USE, not directly after you get home from shopping!!!) and also wash your hands afterwards so you don't ingest the toxins via your skin.