A reliable odometry source is a prerequisite to enable complex autonomy behaviour in next-generation robots operating in extreme environments. In this work, we present a high-precision lidar odometry system to achieve robust and real-time operation under challenging perceptual conditions. LOCUS (Lidar Odometry for Consistent operation in Uncertain Settings), provides an accurate multi-stage scan matching unit equipped with an health-aware sensor integration module for seamless fusion of additional sensing modalities. We evaluate the performance of the proposed system against state-of-the-art techniques in perceptually challenging environments, and demonstrate top-class localization accuracy along with substantial improvements in robustness to sensor failures. We then demonstrate real-time performance of LOCUS on various types of robotic mobility platforms involved in the autonomous exploration of the Satsop power plant in Elma, WA where the proposed system was a key element of the CoSTAR team's solution that won first place in the Urban Circuit of the DARPA Subterranean Challenge.