Indoor localization is a cornerstone technology for smart environments, including smart homes, factories, and healthcare systems. Time Difference of Arrival (TDoA) techniques are widely recognized for their high localization accuracy but face significant challenges in managing computational demands and latency, particularly in Internet of Things (IoT) scenarios. This paper introduces the Lyapunov Optimization-based Dynamic Computation Offloading (LODCO) algorithm, a novel framework designed to enhance TDoA localization by leveraging the capabilities of Mobile Edge Computing (MEC). By dynamically balancing computation between edge servers and local devices, LODCO minimizes latency, optimizes energy consumption, and adapts to diverse environmental and user requirements. The proposed algorithm addresses the inherent trade-offs in TDoA localization systems, achieving reduced execution delays and maintaining precise positioning even in ultra-dense network (UDN) environments characteristic of 5G deployments. Extensive simulations demonstrate that LODCO consistently outperforms state-of-the-art algorithms, such as WAKNN-PSO and MLE-PSO, in terms of positioning accuracy, energy efficiency, and bandwidth utilization. These findings highlight the scalability and practicality of LODCO in enabling real-time indoor localization within IoT-driven ecosystems.