In this work we present a Monte Carlo study of proton irradiation of lung parenchyma phantoms for particle energies that are typically used for proton therapy, ranging from 150 to 200 MeV. The Bragg peaks of the proton beams were scored in a water phantom distal to voxelized slabs of lung material. A detailed lung parenchyma phantom was modeled and converted into a voxelized structure, with a resolution similar to that obtained by computed tomography, to study differences in the dose deposited by the proton beams distal to the phantom caused by merging small structures into larger voxels. The results show that the Bragg peak dose in water can vary by up to 11%, the distal edge degradation can be as large as 1.1 mm, and the maximum observed changes in the range at 90% of the dose are 0.4 mm in water. From our results, we conclude that computational proton dose predictions in a lung are associated with large uncertainties. To improve the accuracy of dose calculations, a more detailed model of lung parenchyma is needed.