If both come from Mexico to Europe in the same amount of time on a ship, how do organic limes stay unmoldy while conventional ones need fungicides?
It's a common misconception that organic produce doesn't use any kind of pesticides (insecticide, herbicide or fungicide) or other 'chemicals'. Unless you're buying apples from someone's back yard, there is some form of pesticide on it. Organic produce is simply limited on which types of pesticides they can use. Your limes will certainly have an 'organic' fungicide on them. You can read more about the requirements for calling produce organic in the EU here.