In recent literature, it has been observed that obtaining low overhead LTE downlink scheduling mechanisms that ensure a descent QoS is a challenging task especially in the presence of transient overloads. This paper proposes a novel three level LTE downlink scheduling framework (called TLS). The three major objectives of the proposed framework includes low overall traffic flow selection and mapping overheads at each Transmission Time Interval (TTI), maintaining acceptable QoS levels for various real-time (RT) variable bit rate (VBR) flows even during transient overloads through graceful degradation, and maximizing spectral efficiency by effectively exploiting multi-user diversity. Both the outermost and the second level of TLS employs a novel adjustable frame-based approach to provide efficient service even in the face of ever changing wireless channel conditions, system workloads, traffic bit rates etc. A low-overhead O(1) look-up based scheme is used in the innermost layer of the framework to physically allocate bandwidth resources to the traffic flows at each TTI. Simulation results clearly reveal that TLS outperforms the existing schedulers with respect to QoS, goodput and spectral efficiency.