Using Funnel, measure oil, milk, dressing mix, yogurt, and lemon juice into Cruet. Screw on lid; shake to mix. If making ahead, cover and refrigerate up to five days.
In a bowl, combine 1⁄2 cup dressing and chicken.
Slice avocado. Slice buns open and toast, if desired.
Fill each bun with lettuce, chicken, avocado, and topper. Drizzle with more dressing and top with parmesan cheese, if desired.