The Li-Sn binary system has been the focus of extensive research because it features Li-rich alloys with potential applications as battery anodes. Our present re-examination of the binary system with a combination of machine learning and ab initio methods has allowed us to screen a vast configuration space and uncover a number of overlooked thermodynamically stable alloys. At ambient pressure, our evolutionary searches identified a new stable Li3Sn phase with a large BCCbased hR48 structure and a possible high-T LiSn4 ground state. By building a simple model for the observed and predicted Li-Sn BCC alloys we constructed an even larger viable hR75 structure at an exotic 19:6 stoichiometry. At 20 GPa, new 11:2, 5:1, and 9:2 phases found with our global searches destabilize previously proposed phases with high Li content. The findings showcase the appreciable promise machine learning interatomic potentials hold for accelerating ab initio prediction of complex materials.