Final answer:
The deep pleural membrane that covers the surface of the lungs is called the visceral pleura. It lines and protects the lungs, while reducing friction during breathing.
Step-by-step explanation:
The deep pleural membrane that covers the surface of the lungs is called the visceral pleura. The visceral pleura is the innermost layer of the pleura that is superficial to the lungs and extends into the lung fissures. It is responsible for lining and protecting the lungs, while also reducing friction during breathing.