They have immunity, just as you develop immunity to Chicken Pox if you catch it. But even monitors can get sick when they have a wound. Just as a cut on the hand can get infected, a monitor lizard can get an infection. The first birds appeared during the Jurassic Period. Birds, also, can get sick.
Chickens get a disease called Rous sarcoma, which causes tumors.
A bird called the heath hen used to live in the United States and Canada until it was infected by another chicken disease. After the disease had weakened and killed many heath hens, continued hunting by humans and goshawks drove the heath hen to extinction. Mites and insects may bite the reptiles and spread a disease. That's how mosquitoes spread malaria to humans today. The spread of diseases also seems to be related to weather.