The Herschel Lensing Survey (HLS) will conduct deep PACS and SPIRE imaging of ~40 massive clusters of galaxies. The strong gravitational lensing power of these clusters will enable us to penetrate through the confusion noise, which sets the ultimate limit on our ability to probe the Universe with Herschel. Here, we present an overview of our survey and a summary of the major results from our Science Demonstration Phase (SDP) observations of the Bullet Cluster (z=0.297). The SDP data are rich, allowing us to study not only the background high-redshift galaxies (e.g., strongly lensed and distorted galaxies at z=2.8 and 3.2) but also the properties of cluster-member galaxies. Our preliminary analysis shows a great diversity of far-infrared/submillimeter spectral energy distributions (SEDs), indicating that we have much to learn with Herschel about the properties of galaxy SEDs. We have also detected the Sunyaev-Zeldovich (SZ) effect increment with the SPIRE data. The success of this SDP program demonstrates the great potential of the Herschel Lensing Survey to produce exciting results in a variety of science areas.