Make the curry mayo. In a small bowl, whisk together the mayonnaise, curry paste, and lime juice until smooth.
Make the tempura green beans. In a large bowl, whisk together the flour, club soda, and salt until smooth. Add the green beans and toss until coated.
Attach a deep-fry thermometer to the side of a large, heavy pot. Add the vegetable oil to the pot over medium-high heat. Once the oil reaches 375°F, working in batches, add the battered green beans and cook, turning halfway through, until golden, about 3 minutes. Transfer to a paper towel-lined plate and season with salt to taste. Repeat with the remaining green beans, allowing the oil to return to 375°F between batches.
Serve immediately with the curry mayo on the side for dipping.