Cook the bacon in a medium skillet over medium heat, stirring, until crisp, about 8 minutes. Transfer to a paper towel-lined plate using a slotted spoon.
Whisk the sour cream, mayonnaise and buttermilk in a large bowl. Add the scallions, dill, 1/2 teaspoon salt and a few grinds of pepper; whisk to combine. Add the chicken and half each of the bacon and tomatoes; toss to coat. Add the avocado and gently toss.
Serve the chicken salad in the lettuce leaves; top with the remaining bacon and tomatoes. Serve with the dinner rolls.