Place one radish in a spoon. Using a sharp knife, cut thin slices into the radish. The spoon will stop the knife before it cuts all the way through the radish. Once you have made thin slices, flip the radish, put it back in the spoon, and make additional cuts at a 45-degree angle. Repeat with remaining radishes.
Whisk together olive oil, lemon juice, and Cajun seasoning.