In the last years, LoRa has emerged as a high potential candidate among several standards for the Internet of Things (IoT) subject to an exponential development. LoRa modulation is based on a classical chirp spread-spectrum technique and permits wireless data transmission up to 50 kbps over several kilometers with a high energy efficiency. Although a well-known principle, its performance in terms of symbol or bit error probability has been theoretically analyzed in few recent papers only. Recently, closed-form approximations of Bit Error Probability (BEP) for additive white Gaussian noise channels and Rayleigh fading channels were proposed. In this paper, we introduce a new approach using Marcum function for approximating the LoRa BEP. The latter is available for both Additive White Gaussian Noise channels and Rayleigh fading channels and the approach should deal with a variety of fadings. Simulations and comparisons with the state of the art show that the proposed approximation is almost ten times more accurate and may be considered as a numerical reference.