Light Detection and Ranging (LiDAR) sensors have become a de-facto sensor for many robot state estimation tasks, spurring development of many LiDAR Odometry (LO) methods in recent years. While some smoothing-based LO methods have been proposed, most require matching against multiple scans, resulting in sub-real-time performance. Due to this, most prior works estimate a single state at a time and are ``submap''-based. This architecture propagates any error in pose estimation to the fixed submap and can cause jittery trajectories and degrade future registrations. We propose Fixed-Lag Odometry with Reparative Mapping (FORM), a LO method that performs smoothing over a densely connected factor graph while utilizing a single iterative map for matching. This allows for both real-time performance and active correction of the local map as pose estimates are further refined. We evaluate on a wide variety of datasets to show that FORM is robust, accurate, real-time, and provides smooth trajectory estimates when compared to prior state-of-the-art LO methods.