We propose a novel framework for distributed,multi-robot SLAM intended for use with 3D LiDAR observations. The framework, DiSCo-SLAM, is the first to use the lightweight Scan Context descriptor for multi-robot SLAM, permitting a data-efficient exchange of LiDAR observations among robots. Additionally, our framework includes a two-stage global and local optimization framework for distributed multi-robot SLAM which provides stable localization results that are resilient to the unknown initial conditions that typify the search for inter-robot loop closures. We compare our proposed framework with the widely used distributed Gauss-Seidel (DGS) approach, over a variety of multi-robot datasets, quantitatively demonstrating its accuracy, stability, and data-efficiency.