Capacity Expansion Planning (CEP) addresses the strategic decision-making process for determining the optimal combination of generation and transmission investments to meet future electric energy demand under uncertainty. This problem is usually formalized as a two-stage stochastic mixed-integer program (SMIP). The resultant large-scale SMIP often becomes computationally formidable for real-sized systems and numerous scenarios. To address this challenge, we introduce a novel scenario-wise decomposition and parallelization strategy based on Lagrangian Relaxation. We begin by validating the proposed methodology using two small-scale test systems, comparing its solutions with those derived from solving the full problem. Subsequently, we assess the computational performance of our approach for an instance of the Chilean National Electrical System where the problem complexities render its direct solution unfeasible. Our proposed algorithm not only achieves feasibility in handling large-scale SMIPs but also provides satisfactory solutions for intricate problems that would otherwise be challenging to solve directly using conventional solvers.