In food processor, process cannellini beans, garlic, lemon juice, olive oil and basil pesto with on-and-off pulses until mixture is smooth. Season with salt and pepper to taste.
Transfer mixture to medium bowl. Cover with plastic wrap; refrigerate until ready to use.
To make sandwiches, spread about 1 tablespoon White Bean and Pesto Spread onto each slice of bread. Divide chicken among 8 of the bread slices.
Arrange lettuce on remaining 8 bread slices. Place lettuce-topped bread slices upside-down over chicken.
Cut sandwiches in half.