In this work, we examine the performance of the LoRa chirp spread spectrum modulation in the presence of both additive white Gaussian noise and interference from another LoRa user. To this end, we extend an existing interference model to the more realistic case where the interfering user is neither chip- nor phase-aligned with the signal of interest and we derive an expression for the SER. We show that the existing interference model overestimates the effect of interference on the error rate. Moreover, we derive a low-complexity approximate formula that can significantly reduce the complexity of computing expression.