Around the Late Triassic period, animals with Carrier's constraint were preyed on by bipedal species that evolved a more efficient stride
Sea snakes have only one lung.
Monitor lizards increase their stamina by using bones and muscles in the throat and floor of the mouth to "gulp" air.
Crocodilians have three modes of locomotion: crawling for short distances (this sprawling gait is subject to Carrier's Constraint); "high walk" for longer distances (the erect limb posture minimizes sideways flexing); "gallop" in emergencies (avoids Carrier's Constraint but they can only gallop for a few seconds).
Birds have erect limbs and rigid bodies, and therefore do not flex sideways when moving. In addition many of them have a mechanism which pumps both lungs simultaneously when the birds rock their hips.
Most mammals have erect limbs and flexible bodies, which makes their bodies flex vertically when moving fast. This aids breathing as it expands and compresses both lungs simultaneously.