1. Add the vinegar, lemon juice, garlic, pepper and salt to a blender. Pulse several times to mix well. With the blender running constantly, add the evoo slowly in a thin stream, continue blending until the oil and acids are completely emulsified and creamy-looking. Set vinaigrette aside.
2. Place the bacon strips on a cold, non-stick skilled and place over medium heat. Cook the bacon slowly, turning often, until nicely browned but not too crispy.
3. Meanwhile, place the chicken breasts between two large sheets of plastic wrap, and pound them with a mallet until they are uniformly 1/4 inch thick.
4. When the bacon strips are finished cooking, place them between paper towels to drain. Add a splash of olive oil to the skillet, and increase the heat to medium-high (turn the heat down if the bacon fat begins to smoke).
5. Brown the chicken for 2-3 minutes per side, just until cooked through. Transfer chicken to a plate and keep warm under foil.
6. Core the lettuce, tear into bite-sized pieces, wash under cold water, spin dry, and place in a very large bowl.
7. Add the sliced onion, tomatoes, and 6 tbsp of vinaigrette (more or less to taste). Toss the salad well to evenly distribute the dressing and vegetables.
8. Dive the salad between two large plates. Cut the chicken breasts into bite-sized pieces and place over salad.
9. Core, peel and slice the avocado and add half to each salad. Chop the bacon and sprinkle evenly over the two salads. Serve immediately.