Maximizing the network lifetime is one of the major challenges in Low Power and Lossy Networks (LLN). Routing plays a major role in LLN, for minimizing the energy consumption across the network nodes. IPv6 Routing Protocol for Low Power and Lossy Networks (RPL) is a standardized routing protocol for LLN. Though, RPL fulfilled the necessity of LLN, several issues like increasing the energy efficiency, quality of service and the network lifetime are to be focused. In LNN, the inefficient route selection results in increased network traffic, energy depletion and packet loss ratio across the network. In this paper, we propose a fuzzy logic based energy aware routing protocol (FLEA-RPL), which considers the routing metrics load, residual energy (RER) and expected transmission count (ETX) for the best route selection. FLEA-RPL applies fuzzy logic over these metrics, to select the best route to transfer the network data efficiently. The COOJA simulator is used to assess the efficiency of the proposed FLEA-RPL. The FLEA-RPL protocol is compared with similar protocol standard RPL, MRHOF (ETX) based RPL (MRHOF-RPL) and FL-RPL. The simulation result shows that FLEA-RPL improves the network lifetime by 10-12% and packet delivery ratio by 2-5%.