Rapid kV cone-beam computed tomography (CBCT) scans are achievable in under 20 s on select linear accelerator systems to generate volumetric images in three dimensions (3D). Daily pre-treatment four-dimensional CBCT (4DCBCT) is recommended in image-guided lung radiotherapy to mitigate the detrimental effects of respiratory motion on treatment quality. To demonstrate the potential for thoracic 4DCBCT reconstruction using projection data that was simulated using a clinical rapid 3DCBCT acquisition protocol. We simulated conventional (1320 projections over 4 min) and rapid (491 projections over 16.6 s) CBCT acquisitions using 4D computed tomography (CT) volumes of 14 lung cancer patients. Conventional acquisition data were reconstructed using the 4D Feldkamp-Davis-Kress (FDK) algorithm. Rapid acquisition data were reconstructed using 3DFDK, 4DFDK, and Motion-Compensated FDK (MCFDK). Image quality was evaluated using Contrast-to-Noise Ratio (CNR), Tissue Interface Width (TIW), Root-Mean-Square Error (RMSE), and Structural SIMilarity (SSIM). The conventional acquisition 4DFDK reconstructions had median phase averaged CNR, TIW, RMSE, and SSIM of 2.96, 8.02mm, 83.5, and 0.54, respectively. The rapid acquisition 3DFDK reconstructions had median CNR, TIW, RMSE, and SSIM of 2.99, 13.6mm, 112, and 0.44 respectively. The rapid acquisition MCFDK reconstructions had median phase averaged CNR, TIW, RMSE, and SSIM of 2.98, 10.2mm, 103, and 0.46, respectively. Rapid acquisition 4DFDK reconstruction quality was insufficient for any practical use due to sparse angular projection sampling. Results suggest that 4D motion-compensated reconstruction of rapid acquisition thoracic CBCT data are feasible with image quality approaching conventional acquisition CBCT data reconstructed using standard 4DFDK.