Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this talk I'm going to introduce both and show how they can be considered a special case of an overarching fibrational construction, generalizing Hofstra's construction of Dialectica fibrations. At its highest level of generality, it's a construction that turns a tower of fibrations into another tower of fibrations by twisting each of the components using the opposite fibration construction.