Process cookies in a food processor until coarse crumbs. Transfer to a bowl; stir in butter. Press mixture firmly into a 10-inch pieplate.
Combine banana and lemon juice, if desired. Arrange banana over crust. Cover and freeze until firm.
Beat 1/4 cup whipped topping, ice cream, and next 3 ingredients at medium speed with a mixer until blended. Add 1/2 cup pecans. Spread over crust; cover and freeze 8 hours.
Spread remaining whipped topping over pie; top with syrup and 2 tablespoons pecans.