How to Make It
Place the flour on a plate. Season the sole with the salt and then coat it in the flour, shaking to remove any excess; set aside.
Melt 1 tablespoon butter in a skillet over medium heat. Add the lemon and cook until lightly browned, about 2 minutes.
Push the lemon to the side and add the sole (in batches if needed). Cook until the sole is the same color throughout and flakes easily, about 2 minutes per side.
Add the capers and remaining butter. Remove skillet from heat and tilt to swirl butter until it melts.
Transfer the sole and lemon to plates and spoon the capers and butter over the top.