Or out on the counter?
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Merrill is a co-founder of Food52.
I store my citrus in the refrigerator, but that's more for space reasons than anything else. I think limes will last nearly as long without shriveling up and drying out at room temperature as they would in the fridge, although I haven't done a comparison test!
Chris is a trusted source on General Cooking
I never store citrus fruits in the refrigerator. I think they taste better at room temperature.
I store them in the fridge too, that is if I'm not going to eat them in the next few days. As Merrill says, citrus does dry up at room temperature faster. A room temperature citrus fruit is generally going to yield more juice at room temperature than a cold one, so if your limes are in the fridge just take them out a few hours before using them.
It also depends on where you live - I'm in Colorado, which is really dry, so it's essential I store them in the refrigerator if I'm not going to be using them within 1-2 days.