In the evolution of aspiration breathing, the responsibility for lung ventilation gradually shifted from the hyobranchial to the axial musculoskeletal system, with axial muscles taking over exhalation first, at the base of Tetrapoda, and then inhalation as well at the base of Amniota. This shift from hyobranchial to axial breathing freed the tongue and head to adapt to more diverse feeding styles, but generated a mechanical conflict between costal ventilation and high-speed locomotion. Some "lizards" (non-serpentine squamates) have been shown to circumvent this speed-dependent axial constraint with accessory gular pumping during locomotion, and here we present a new survey of gular pumping behavior in the tuatara and 40 lizard species. We observed gular pumping behavior in 32 of the 40 lizards and in the tuatara, indicating that the ability to inflate the lungs by gular pumping is a shared-derived character for Lepidosauria. Gular pump breathing in lepidosaurs may be homologous with buccal pumping in amphibians, but non-ventilatory buccal oscillation and gular flutter have persisted throughout amniote evolution and gular pumping may have evolved independently by modification of buccal oscillation. In addition to gular pumping in some lizards, three other innovations have evolved repeatedly in the major amniote clades to circumvent the speed-dependent axial constraint: accessory inspiratory muscles (mammals, crocodylians and turtles), changing locomotor posture (mammals and birds) and respiratory-locomotor phase coupling to reduce the mechanical conflict between aspiration breathing and locomotion (mammals and birds).