Almost always. Consumption of oxygen increases greatly during sepsis and the ability of the lung to exchange oxygen frequently falls. The immune system requires excessive amounts of energy which is supplied by oxygen in part, and the lungs often can't meet the demand. Also sometimes the lungs themselves are the source of sepsis such as in pneumonia which further impairs their ability to supply oxygen.
Yes. Sepsis is the body's generalized inflammatory response to a specific infection. Even if the actual infection is not in a patient's lungs, many patients will experience lung injury due to the inflammatory response. The blood vessels also become "leaky" during sepsis, so edema can build in the lungs and further impair oxygenation. For severe sepsis, a breathing machine is not uncommon for a time.