How compromised would your lung function have to be to be turned down from surgery?

Depends: Compromised lung function is serious. Once placed on a breathing machine/respirator for the anesthesia, there needs to be a reasonable chance the patient will come off the ventilator, be able to recover and receive the benefit of the surgery. It is this risk that usually leads to the recommendation to avoid ventilator. Okay to ask your doc the results of your pft/pulmonary function test.

Type of surgery?: Today, we can give anesthesia safely even to patients with severe lung disease. However, the decision to operate will depend on the type of surgery. Ankle surgery, for instance, could be done under spinal anesthesia and wouldn't affect the lungs. Surgery for lung cancer would be much higher risk. Consult a physician anesthesiologist to discuss the specific surgery and risks.