We report on the structural, magnetic, and electronic properties of two new double-perovskites synthesized under high pressure, Pb₂CaOsO₆ and Pb₂ZnOsO₆. Upon cooling below 80 K, Pb₂CaOsO₆ simultaneously undergoes a metal-to-insulator transition and develops antiferromagnetic order. Pb₂ZnOsO₆, on the other hand, remains a paramagnetic metal down to 2 K. The key difference between the two compounds lies in their crystal structures. The Os atoms in Pb₂ZnOsO₆ are arranged on an approximately face-centered cubic lattice with strong antiferromagnetic nearest-neighbor exchange couplings. The geometrical frustration inherent to this lattice prevents magnetic order from forming down to the lowest temperatures. In contrast, the unit cell of Pb₂CaOsO₆ is heavily distorted up to at least 500 K including antiferroelectriclike displacements of the Pb and O atoms despite metallic conductivity above 80 K. This distortion relieves the magnetic frustration, facilitating magnetic order which, in turn, drives the metal-insulator transition. Our results suggest that the phase transition in Pb₂CaOsO₆ is spin driven and could be a rare example of a Slater transition.