Low-Earth Orbit(LEO) satellites have the characteristic of global coverage. The Long Range(LoRa) network based on LEO satellite Internet of Things(IoT) has become a research hotspot. To address the floor effect issue of LoRa modulation schemes in LEO satellite channels, two differential LoRa demodulation strategies are proposed for the differential LoRa modulation scheme. Firstly, a closed-form expression for the Symbol Error Rate(SER) is derived under the LEO satellite channel with dynamic Doppler frequency shift, illustrating the floor effect issue of LoRa modulation in LEO satellite channels. Subsequently, the derived closed-form SER expression is validated using Monte Carlo simulations, and the Bit Error Rate(BER) performance of LoRa modulation and the proposed differential LoRa modulation is evaluated. Simulation results show that compared with the LoRa modulation scheme, differential LoRa modulation and the proposed differential LoRa demodulation strategies can effectively improve the BER performance of LEO satellite IoT under dynamic Doppler frequency offset scenarios.