Due to the worldwide shortage of deceased donor organs for transplantation, tissue/organ donations from living donors became a significant source of transplant organs for various organs including kidneys, livers, and lungs. However, not all willing living donors can donate to their intended patients due to medical incompatibility between the donor and the patient. For any organ with living donor transplantation, such incompatibilities can be overcome by an exchange (of donors) between patients with incompatible donors. Such exchanges became widespread in the last decade for kidneys with the introduction of optimization and market design techniques to kidney exchange. Following the success of kidney exchange, a small but growing number of liver exchanges are also conducted. However, even though living donor lung transplantation is introduced more than two decades ago, lung exchange is neither practiced nor introduced. From an organizational perspective living donation is more involved for lungs than kidneys or livers for it often requires two donors. While this makes living donation more difficult for the lungs, it also means that the role of exchange might be more prominent for living donor lung transplantation. We introduce lung exchange as a novel transplantation modality, develop an an analytical lung exchange model, and introduce optimal lung exchange mechanisms under various logistical constraints. Our simulations suggest that the number of living donor lung transplants can be doubled by allowing 2-way and 3-way exchanges alone, and can be tripled in the absence of logistical constraints.