Lung stiffness is a potential biomarker for multiple lung diseases. MR elastography (MRE) allows non-invasive measurement of lung stiffness. However, it is challenging to estimate stiffness using direct Helmholtz inversion due to low signal-to-noise ratio (SNR) from lung MRE. In this work, a compressed-sensing-based Helmholtz inversion is proposed where noise is reduced via Laplacian of Gaussian (LoG) and Morozov’s discrepancy principle, while the sparsity of stiffness map is explored in a wavelet domain. Results demonstrated that the proposed inversion yielded robust stiffness estimation and successfully detected higher stiffness at total lung capacity (TLC) compared to residual volume (RV).