This paper addresses the issue of quality of service routing optimization within the Internet of Things networks. We particularly focus on the energy-aware and the lightweight aspects. By recognizing the relationship between lightweight and energy-aware routing, we set out to study their combined benefits. This study aims to enhance the Routing Protocol for Low Power and Lossy Networks by integrating energy-awareness and lightweight characteristics based on the Particle Swarm Optimization algorithm. Our approach addresses energy consumption, routing overhead and decision complexity in route establishment. The principal contributions include the introduction of an objective function that considers Expected Life Time, Delay and a new proposed metric Energy Aware-Expected Transmission Count. The improvement of the Long Short Term Memory predicting inertia weight based PSO with Online Gradient Descent that is used to optimize both the parent selection process and Trickle Timer mechanism. The controlled parent switching process to solve unnecessary and frequent changes. Our approach is validated through simulations in Contiki COOJA, with thorough comparisons with some existing protocols based on packet delivery ratio, average energy consumption, convergence time, control overhead, average end-to-end delay and average parent switching as performance metrics. The results reveal that our approach performs better. Depending on the protocol used for comparison, our approach reduced parent switching by 42.59-61.73%, convergence time by 20.31-66.06%, control overhead by 14.4-23.64%, energy consumption by 29.86-49.6%, end-to-end delay by 7.66-40.81% and increased packet delivery ratio by 2-42.92%.