In Lunar Internet of Things (lOT), many mobile devices need to perform various tasks, but computing and storage resources of devices in Lunar lOT are seriously limited. In this paper, we propose a joint edge computing and caching based on Dueling Double Deep Q Network (D3QN) and address the joint edge computing and caching problem for multi-task in Lunar lOT. Firstly, computation offloading and caching of tasks are modeled as a problem of maximizing system revenue, and subject to constraints on latency, energy consumption and cache space of the system. Secondly, D3QN and cache models are used to solve the proposed non-convex optimization problem, and e-greedy strategy is used to select the optimal resource allocation action. In addition, we propose two cache models, namely active cache based on popularity and passive cache based on D3QN. Finally, simulation results show that the proposed algorithm has good performance in terms of latency and energy consumption. Compared with Deep Q Network, Double Deep Q Network and Dueling Deep Q Network, the system revenue of the proposed algorithm is improved by 65%, 35% and 66% respectively.