This letter studies the performance of a single gateway LoRa system in the presence of different interference considering the imperfect orthogonality effect. It utilizes concepts of stochastic geometry to present a low-complexity approximate closed-form model for computing the success and coverage probabilities under these challenging conditions. Monte Carlo simulation results have shown that LoRa is not as theoretically described as a technology that can cover few to ten kilometers. It was found that in the presence of the combination of signal-to-noise ratio (SNR) and imperfect orthogonality between spreading factors (SF), the performance degrades dramatically beyond a couple of kilometers. However, better performance is observed when perfect orthogonality is considered and SNR is not included. Furthermore, the performance is annulus dependent and slightly improves at the border of the deployment cell annuli. Finally, the coverage probability declines exponentially as the average number of end devices grows.