Prepare the grill for direct cooking over medium heat (350-450 degrees) and preheat a grill pan.
In a blender or food processor, pulse the lemon juice, garlic, mustard, Worcestershire, salt, and pepper until smooth. With the machine running, slowly add the olive oil in a steady stream until dressing is emulsified.
In a medium bowl toss the tomatoes and bread cubes with 2 tablespoons of the dressing.
Pour 2 tablespoons of the dressing over chicken and turn to coat evenly.
Brush the cooking grates clean. Grill chicken over direct medium heat, with the lid closed as much as possible, until the meat is firm to the touch and opaque all the way to the center, 8-12 minutes, turning once or twice. The chicken should reach an internal temperature of 165 degrees. During the last 2-3 minutes of grilling, spread the tomatoes and bread cubes in a single layer on the grill pan and cook until the tomatoes start to blister and the bread is toasted, turning occasionally. Remove everything from the grill and let the chicken rest for 3-5 minutes so the juices inside can redistribute. Cut the chicken crosswise into 1/2-inch slices.
In a large bowl toss the lettuce with the dressing a cheese. Divide the salad chicken, tomatoes, and croutons evenly among serving plates. Serve immediately.