1. Combine radishes, 2 teaspoons juice, and 1/4 teaspoon salt in a bowl; toss. Cover and chill at least 30 minutes.
2. Place eggs in a medium saucepan, and cover with cold water to 1 inch above eggs; bring to a boil. Reduce heat, and simmer 10 minutes. Place eggs in ice water, and cool completely. Gently crack eggshells; peel under cold running water. Cut each egg in half lengthwise. Remove yolks. Press yolks through a sieve into a bowl. Set aside 1 tablespoon yolks. Combine remaining 1 teaspoon juice, remaining yolks, 1/4 teaspoon salt, and pepper in a bowl; gradually add oil, stirring well with a whisk until oil is incorporated. Stir in yogurt. Add crabmeat, celery, and mustard; stir gently until combined. Taste crab filling and adjust seasoning, if necessary.
3. Arrange a fan of 3 lettuce leaves on each of 8 plates. Cut a thin slice from the bottom of each egg white half to help them sit flat. Pile the crab filling evenly into egg white halves. Place 2 egg white halves on each plate to one side of lettuce. Sprinkle reserved 1 tablespoon yolk over egg white halves. Arrange 1/4 cup radish mixture on the other side of each serving.