This paper presents a continuous-time lidar-inertial odometry (CT-LIO) system named SLICT2, which improves upon previous methods by using a linear solver from the Eigen library for efficient optimization. Unlike traditional nonlinear solvers, SLICT2 achieves real-time performance with high control point density and competitive accuracy in dynamic scenarios. The system uses internal feature association between iterations, allowing convergence in just a few steps. The key innovations include a more efficient CT-LIO pipeline based on linear solvers and internal association, a detailed formulation of residuals and Jacobians for B-spline control points, and extensive experiments showing SLICT2's competitive performance against state-of-the-art CT-LIO methods. The system is implemented with a custom solver that performs feature association after each incremental step, achieving up to 8 times faster performance than nonlinear solvers. The paper also discusses the computational efficiency of the system, demonstrating that it can handle a large number of lidar factors without compromising performance. The source code is available for community use. The results show that SLICT2 outperforms other methods in accuracy and efficiency, particularly in challenging environments. The system is designed to be easily extendable for applications such as online calibration, temporal offset estimation, and multi-modal sensor fusion.This paper presents a continuous-time lidar-inertial odometry (CT-LIO) system named SLICT2, which improves upon previous methods by using a linear solver from the Eigen library for efficient optimization. Unlike traditional nonlinear solvers, SLICT2 achieves real-time performance with high control point density and competitive accuracy in dynamic scenarios. The system uses internal feature association between iterations, allowing convergence in just a few steps. The key innovations include a more efficient CT-LIO pipeline based on linear solvers and internal association, a detailed formulation of residuals and Jacobians for B-spline control points, and extensive experiments showing SLICT2's competitive performance against state-of-the-art CT-LIO methods. The system is implemented with a custom solver that performs feature association after each incremental step, achieving up to 8 times faster performance than nonlinear solvers. The paper also discusses the computational efficiency of the system, demonstrating that it can handle a large number of lidar factors without compromising performance. The source code is available for community use. The results show that SLICT2 outperforms other methods in accuracy and efficiency, particularly in challenging environments. The system is designed to be easily extendable for applications such as online calibration, temporal offset estimation, and multi-modal sensor fusion.