Considering energy as a crucial resource, several duty cycle based MAC have already been proposed for Wireless Sensor Networks (WSNs) to gain higher energy efficiency during long idle period of the sensors, and are optimized for light traffic loads. Contrastively, considering the bandwidth constraint of WSNs, and to optimize the heavy traffic loads, another research trend is continuing in devising rate and congestion control at the MAC layer. To provide an integrated solution of both these distinct research trends at the MAC layer, in this paper, we present a Load-independent Energy-efficient and Rate-control Integrated Asynchronous Duty Cycle MAC (LER-MAC) for WSNs. Performance of LER-MAC has been evaluated using ns-2 which demonstrates that, LER-MAC conserves energy considerably during light traffic loads along with procures higher throughput and lower latency avoiding packet drops through maximum utilization of the channel during heavy traffic loads.