Bring broth, water and bay leaf to a gentle simmer in a wide skillet. Add turkey, cover partly and poach over low heat for 8 to 12 minutes, turning once, until the centers reach 165°F.
Transfer turkey to a shallow container with 2 tablespoons of the poaching liquid. Cool for 5 minutes and refrigerate promptly for 30 minutes, then slice thinly across the grain.
Meanwhile, heat oven to 400°F and bake bacon on a rimmed sheet pan for 15 to 20 minutes until crisp. Drain and cool on paper towels.
Mash avocado with mayonnaise, lemon juice, salt and pepper until mostly smooth. Split the rolls, toast their cut faces briefly under the broiler and cool on a rack.
Spread avocado mayonnaise over the cut faces. Layer dry iceberg, thin turkey slices, blotted tomato and two bacon slices into each roll, breaking bacon only as needed to fit the length.
Close the subs and cut across the middle. Serve cold, one per person, or refrigerate covered until eating later the same day.