Avocado Blts on Toasted Oatmeal Bread

• 2 to 3 tomatoes (preferably heirloom), thickly sliced
• Salt and freshly ground black pepper to taste
• 4 leaves fresh basil, torn roughly
• 2 tablespoons extra-virgin olive oil
• 1 very ripe avocado
• 4 tablespoons mayonnaise
• Juice of 1/2 lemon
• 4 slices soft oatmeal or oat-nut bread, toasted
• 6 slices thick-cut bacon, cooked until crisp
• 1 head Boston or butter lettuce, leaves separated