Purpose: The primary objective of our study was to perform a quantitative robustness analysis of the dose-averaged linear energy transfer (LETd) and related RBE-weighted dose in robustly optimized (in terms of the range and set up uncertainties) pencil beam scanning (PBS) proton lung cancer plans. Methods: In this study, we utilized the 4DCT dataset of six anonymized lung patients. PBS lung plans were generated using a robust optimization technique (range uncertainty: ��3.5% and setup errors: ��5��mm) on the CTV for a total dose of 5000 cGy (RBE) in five fractions using the RBE of 1.1. For each patient, the LETd distributions were calculated for the nominal plan and three groups. Group 1: two plan robustness scenarios for range uncertainties of ��3.5%; Group 2: twelve plan robustness scenarios (range uncertainty (��3.5%) in conjunction with setup errors (��5��mm)); and Group 3: ten different breathing phases of the 4DCT dataset. The RBE-weighted dose to the OARs was evaluated for all robustness scenarios and breathing phases. The variation (���) in the mean LETd and mean RBE-weighted dose from each group was recorded. Results: The mean LETd in the CTV of nominal PBS lung plans among six patients ranged from 2.2 to 2.6��keV/��m. On average, for the combined range and setup uncertainties, the ��� in the mean LETd among 12 scenarios of all six patients was 0.6��keV/��m, which is slightly higher than when only the range uncertainties were considered (0.4��keV/��m). The ��� in the mean LETd in a patient was ���1.7��keV/��m in the heart and ���1.2��keV/��m in the esophagus and total lung. The ��� in the mean RBE-weighted dose in a patient was up to 79 cGy for the total lung, 165 cGy for the heart, and 258 cGy for the esophagus. For ten breathing phases, the ��� in the mean LETd in a patient was ���0.3��keV/��m in the CTV, ���0.5��keV/��m in the heart, ���0.4��keV/��m in the esophagus, and ���0.7��keV/��m in the total lung. Conclusion: The addition of setup errors to the range uncertainties resulted in slightly less homogeneous LETd distributions. The variations in the mean LETd among the ten breathing phases were slightly larger in the total lung than in the heart and esophagus. The combination of setup and range uncertainties had a greater impact than the effect of breathing phases on the variations in the mean RBE-weighted dose to the OARs. Overall, the LETd distributions in the CTV were less sensitive than those in the OARs to setup errors, range uncertainties, and breathing phases for robustly optimized (in terms of range and setup uncertainities) PBS proton lung cancer plans.