Combine lettuce, chicken, black olives, green bell pepper, red bell pepper, and red onion together in a bowl; cover with plastic wrap and refrigerate until chilled, about 30 minutes.

Mix oil, red wine vinegar, lemon juice, sugar, salt, pepper, and garlic in a container with lid; cover and shake until well combined. Refrigerate until chilled, about 30 minutes.

Mix avocado into salad. Shake dressing and drizzle over salad; toss lightly.