In this work we study the offloading decision and computing resource allocation of tasks generated by internet-of-medical-things (IoMT) devices into a non-terrestrial network, comprised of local coordinating low-altitude platforms (LAPs) working also as multi-access edge computing (MEC) servers, and a common low Earth-orbit (LEO) satellite, which acts as a common MEC server across the LAPs. We solve the problem of total delay minimization across the tasks in the system. Given the NP-hard nature of the offloading decision problem, we solve it with a sequential greedy heuristic. To avoid biasing the offloading decision due to the computing resource initialization, weformulate a mechanism for dynamically initializing the resources at each step. We propose several methods for the computing resource initialization, and show in simulations, regions where each method is the most effective depending on the parameters of the system.