1. Cook bacon in a 12-inch heavy skillet over medium heat until crisp, then transfer to paper towels to drain.
2. Meanwhile, purée avocado, mayonnaise, 1/3 cup water, lemon juice, and 1/4 teaspoon each of salt and pepper in a blender until smooth, thinning with water if necessary.
3. Heat grill pan over medium-high heat until hot.
4. Brush cut sides of bread with some of oil. Grill bread, cut sides down, until grill marks appear, about 3 minutes, then cut into 1-inch pieces.
5. Toss turkey with remaining oil and 1/4 teaspoon each of salt and pepper. Grill turkey, turning once, until just cooked through, about 3 minutes total, then cut into 1-inch strips.
6. Toss romaine, cabbage, tomatoes, and croutons in a large bowl, then top with turkey, crumbled bacon, and a dollop of dressing.
7. Toss just before serving and serve remaining dressing on the side.