The highly complex structure of railway train timetables limits frequent adjustments, while fluctuating passenger demand often necessitates such modifications. To cope with this challenge, railway companies design implementable train timetables one to three months in advance by scheduling additional trains and adjusting existing ones based on a baseline train timetable. This study addresses this practical problem through the integrated optimization of line planning and additional trains scheduling (ILPATS). We propose a new integer linear programming (ILP) model that minimizes the weighted sum of railway operator and passenger costs. Leveraging the characteristics of the model, a Lagrangian relaxation-based algorithm is designed, which dualizes track capacity and coupling constraints decomposing the original problem into a line planning subproblem and a set of train-specific subproblems. A novel unit dual cost sorting strategy is further introduced to enhance computational performance. A set of numerical experiments is conducted on both small-scale and large-scale instances designed based on the Chinese high-speed railway corridors to evaluate the effectiveness and computational efficiency of the proposed model and algorithm. The results demonstrate that the Lagrangian relaxation-based algorithm effectively solves all instances. For the large-scale instances, it achieves an average optimality gap of 0.98%, and improves the quality of the upper bound solutions by an average of 3.64% compared to the sequential solving method, with an average computational time of 146.78 min. Furthermore, based on the experimental results, it is recommended that railway operators minimize adjustments to high-priority trains and prioritize long-distance passenger demand when scheduling additional services.