This paper presents a semi-analytical approximation of Symbol Error Rate (SER) for the well known LoRa Internet of Things (IoT) modulation scheme in the following two scenarios: 1) in multi-path frequency selective fading channel with Additive White Gaussian Noise (AW GN) and 2) in the presence of a second interfering LoRa user in flat-fading AW GN channel. Performances for both coherent and non-coherent cases are derived by considering the common Discrete Fourier transform (DF T) based detector on the received LoRa waveform. By considering these two scenarios, the detector exhibits parasitic peaks that severely degrade the performance of the LoRa receiver. We propose in that sense a theoretical expression for this result, from which a unified framework based on peak detection probabilities allows us to derive SER, which is validated by Monte Carlo simulations. Fast computation of the derived closedform SER allows to carry out deep performance analysis for these two scenarios.