In a small bowl, combine the paprika, onion powder and salt; rub over chicken. Using long-handled tongs, moisten a paper towel with cooking oil and lightly coat the grill rack.
Grill chicken, uncovered, over medium heat or broil 4 in. from the heat for 3 to 4-1/2 minutes on each side or until a thermometer reads 170°. When cool enough to handle, cut chicken into cubes.
In a large bowl, whisk mayonnaise and lemon juice until smooth. Stir in the chicken, apples, cranberries and onion. Serve on lettuce-lined plates.