Coddling the egg makes it creamy but does not heat it to 160°, the temperature required to kill bacteria. Use a pasteurized whole egg if you have safety concerns.
Place egg in a small bowl or coffee mug; cover with boiling water. Let stand 1 minute. Rinse egg with cold water; break egg into a small bowl.
Combine pepper and next 3 ingredients (through garlic) in a mini food processor; process until minced. Add egg and juice; process 1 minute or until thick. Gradually add oil and 1 tablespoon water, processing until blended.
Combine croutons, lettuce, Lemon-Grilled Chicken Breasts, and egg mixture in a large bowl; toss gently. Divide salad evenly among 4 plates. Sprinkle each serving with 1 tablespoon cheese.