In this paper, we analyse the reliability performance for the orthogonal time frequency space (OTFS) based low earth orbit (LEO)-satellite-air-terrestrial (LSAT) communication system. To facilitate the downlink transmission from the LEO satellite to the terrestrial node, a group of randomly distributed mobile unmanned aerial vehicles (UAVs) are employed to serve as the relays with decode-and-forward (DF) scheme. With the aid of stochastic geometry approach, the distribution of mobile UAVs is modeled by Poisson point processes (PPP) process with two motion modes: user dependent model (UDM) and user independent model (UIM). We derive the approximate closed-form expressions for the outage probabilities of the LSAT system under two UAV motion modes. Finally, the simulation results demonstrate that the reliability of the LSAT system can be significantly enhanced by using OTFS scheme, and by properly adjusting the UAV deployment parameters, corroborating the theoretical derivation.