Heat grill to medium.

Rub chicken with ½ teaspoon olive oil and sprinkle with ¼ teaspoon each salt and pepper. Grill until instant-read thermometer registers 165°F, 8 to 10 minutes per side. Transfer to cutting board and let rest 10 minutes before slicing.

While chicken is grilling, grill lemon halves and baguette, cut sides down, until charred, 2 to 3 minutes. Transfer to cutting board. Rub cut side of baguette with garlic clove.

Squeeze 2 tablespoons juice from grilled lemon halves into small bowl and whisk in mayonnaise, Dijon, and anchovy paste, then gradually whisk in remaining 2 tablespoons oil until thoroughly incorporated.

In large bowl, toss romaine and celery with ¼ cup dressing and ¼ teaspoon pepper to coat, then toss with Parmesan and another ¼ teaspoon pepper.

Drizzle remaining dressing on baguette and layer with sliced chicken, salad, and tomatoes. Cut each in half to make 4 sandwiches.