LiDAR-inertial odometry is widely used in robotics navigation, autonomous driving, and drone operation to provide precise, low-latency motion estimation. Filter-based methods are fast but suffer from significant cumulative errors. Graph optimization methods reduce cumulative errors through loop closure detection but are computationally expensive. In this work, we propose LIO-DPC, a framework that combines the benefits of the filter-based approach and graph-based approach. First, we propose a dynamic pose chain optimization method. It generates an initial pose chain using the fast filter. This is followed by applying computationally efficient local graph optimization to a set of local pose chains to generate refined relative poses, which are then used to update the motion estimation. Second, we propose a loop sparsification approach to select representative loops that are both temporally and spatially proximate, to reduce the computational complexity in graph optimization and minimize loop errors. Extensive experiments demonstrate that LIO-DPC achieves real-time performance and outperforms state-of-the-art methods in accuracy.