Integrating Multi-access Edge Computing (MEC) in Low Earth Orbit (LEO) network enables all user equipment on the ground to receive MEC services with low service latency relatively. Service request scheduling can realize the effective utilization of various resources of the network and the system, and guarantee the performance of the network system. Service deployment and service request scheduling are closely related. Therefore, the joint service deployment and service request scheduling problem (SDRS) is modeled as an optimization problem, which is a mixed integer linear programming problem. Our goal is to reduce the proportion of unsatisfactory services while minimizing the transmission cost when deploying services on LEO-MEC nodes, and to use the resolved decision variables to dispatch requests and deploy services. In order to avoid overloading of some nodes and underutilization of other nodes, which would cause the waste of satellite system resources, we modified the MILP and imposed an upper limit on the load that each satellite node can support. The simulation results show that, compared with the baseline mechanism, our proposed mechanism can achieve better performance in terms of service user ratio and computing resource utilization. The newly proposed MILP variant with load balancing (SDRS-LB) has a lower load than the SDRS scheme.