Preheat a grill to medium. In a large pot of boiling, salted water, cook the pasta according to package directions until al dente. Drain in a colander, then rinse with cold water until cool.
Meanwhile, in a medium bowl, whisk together the olive oil, lemon juice and mustard; season with salt and pepper. Reserve half of the vinaigrette for serving and stir in the sliced basil leaves. Brush some of the remaining vinaigrette onto the mushroom caps, then add the chicken cutlets to the bowl and toss.
Arrange the chicken and mushrooms on the cooking grate, cover and grill, turning once, until golden-brown and cooked through, about 6 minutes for the mushrooms and 8 minutes for the chicken. Let stand for 10 minutes before thinly slicing the mushrooms and chicken.
Arrange the lettuce leaves, pasta, chicken, mushrooms, tomato and whole basil leaves on a large platter; serve with the reserved vinaigrette.