Rapid repurposing of existing drugs as new therapeutics for COVID-19 has been an important strategy in the management of disease severity during the ongoing SARS-CoV-2 pandemic. Here, we used high-throughput docking to screen 6000 compounds within the DrugBank library for their potential to bind and inhibit the SARS-CoV-2 3 CL main protease, a chymotrypsin-like enzyme that is essential for viral replication. For 19 candidate hits, parallel in vitro fluorescence-based protease-inhibition assays and Vero-CCL81 cell-based SARS-CoV-2 replication-inhibition assays were performed. One hit, diclazuril (an investigational anti-protozoal compound), was validated as a SARS-CoV-2 3 CL main protease inhibitor in vitro (IC₅₀ value of 29 µM) and modestly inhibited SARS-CoV-2 replication in Vero-CCL81 cells. Another hit, lenvatinib (approved for use in humans as an anti-cancer treatment), could not be validated as a SARS-CoV-2 3 CL main protease inhibitor in vitro, but serendipitously exhibited a striking functional synergy with the approved nucleoside analogue remdesivir to inhibit SARS-CoV-2 replication, albeit this was specific to Vero-CCL81 cells. Lenvatinib is a broadly-acting host receptor tyrosine kinase (RTK) inhibitor, but the synergistic effect with remdesivir was not observed with other approved RTK inhibitors (such as pazopanib or sunitinib), suggesting that the mechanism-of-action is independent of host RTKs. Furthermore, time-of-addition studies revealed that lenvatinib/remdesivir synergy probably targets SARS-CoV-2 replication subsequent to host-cell entry. Our work shows that combining computational and cellular screening is a means to identify existing drugs with repurposing potential as antiviral compounds. Future studies could be aimed at understanding and optimizing the lenvatinib/remdesivir synergistic mechanism as a therapeutic option.