Lizards, like many vertebrates, have lungs and a respiratory system that enables them to breathe. They are different from mammals and birds in that they don't have a diaphragm muscle and instead breathe by flexing their body muscles.
Since they need to use their muscles to breathe, lizards typically hold their breath while doing intense activity. Some lizards can bypass this limitation by using their throat muscles to pull air into their lungs during activity.
Not all reptiles use body muscle-based breathing. Crocodiles and turtles have developed different methods for breathing. Crocodiles have a diaphragm which enables them to inhale air, while turtles, whose lung expansion is limited by their shells, have a thin muscle layer that lies on their lungs and expands and contracts to bring in air.