Prepare Rémoulade Dipping Sauce by whisk together all ingredients in a medium bowl. Cover and chill for 1 hour.
Snip off and discard the stalk ends of the green beans; set aside.
Heat the oil to 375 degrees in a deep skillet.
In a large bowl, whisk the beer, salt, and lime juice into the flour until smooth. (The mixture will foam slightly.) Dredge the beans in the batter to coat.
Working in batches, gently place 10 battered beans into the hot oil and let cook for about 1 minute. Using a slotted spoon, transfer the fried beans to a paper bag or paper towel-lined plate to drain and cool. Repeat the process until the remaining the beans are cooked. Serve with Rémoulade dipping sauce and lime wedges.