In the landscape of Long-Term Evolution (LTE) networks, handover algorithms play a pivotal role in maintaining uninterrupted service quality during user mobility. This study revisits the Integrator Handover Algorithm, initially analyzed in previous research, focusing on its optimization in response to the evolving challenges in modern LTE networks. We delve into identifying the inefficiencies of the current algorithm and propose enhancements aimed at improving handover success rates and minimizing latency. Our methodology encompasses a comprehensive literature review, empirical data analysis from contemporary LTE deployments, and a simulation-based approach for algorithm refinement. The outcome is an evolved Integrator Handover Algorithm that is better suited to the high traffic volumes and diverse user behaviors in current LTE network scenarios.