Lung cancer is the leading cause of cancer-related death, and early-stage diagnosis is critical to survival. Biopsy is typically required for a definitive diagnosis, but current low-risk clinical options for lung biopsy cannot access all biopsy sites. We introduce a motion planner for a multilumen transoral lung access system, a new system that has the potential to perform safe biopsies anywhere in the lung, which could enable more effective early-stage diagnosis of lung cancer. The system consists of three stages in which a bronchoscope is deployed transorally to the lung, a concentric tube robot pierces through the bronchial tubes into the lung parenchyma, and a steerable needle deploys through a properly oriented concentric tube and steers through the lung parenchyma to the target site while avoiding anatomical obstacles such as significant blood vessels. A sampling-based motion planner computes actions for each stage of the system and considers the coupling of the stages in an efficient manner. We demonstrate the motion planner's fast performance and ability to compute plans with high clearance from obstacles in simulated anatomical scenarios.