In this work, we study the coded frame error rate (FER) of LoRa under additive white Gaussian noise (AWGN) and under carrier frequency offset (CFO). To this end, we use existing approximations for the bit error rate (BER) of the LoRa modulation under AWGN and we present a FER analysis that includes the channel coding, interleaving, and Gray mapping of the LoRa physical layer. We also derive the LoRa BER under carrier frequency offset and we present a corresponding FER analysis. We compare the derived frame error rate expressions to Monte Carlo simulations to verify their accuracy.