Consider a mobile sensor network that is used to monitor a moving target in a field with obstacles. In this paper, an efficient relocation technique that simultaneously maximizes the network lifetime is proposed. The main sources of energy consumption in the network are sensing, communication, and movement of the sensors. To account for this energy consumption, a graph is constructed with edges that are weighted based on the remaining energy of each sensor. This graph is subsequently employed to address the lifetime maximization problem by solving a sequence of shortest path problems. The proposed technique determines a near-optimal relocation strategy for the sensors as well as an energy-efficient route to transfer information from the target to destination. This near-optimal solution is calculated in every time instant using the information obtained through the previous time step. It is shown that by choosing appropriate parameters, sensors' locations and the communication route from target to destination can be arbitrarily close to their corresponding optimal choices at each time instant. Simulation results confirm the effectiveness of the proposed technique.