In this paper, a new method is proposed based on the auxiliary system approach to investigate lag synchronization between two identical FitzHughNagumo (FHN) neurons with unidirectional coupling. The lag synchronization can be achieved if the synchronization error system between the response and auxiliary systems has an asymptotically stable origin. Different from other studies, the synchronization error system is converted into a set of Volterra integral equations according to the Laplace transform. By using the successive approximation method in the theory of integral equations, an analytical criterion for the detection of lag synchronization between two FHN neurons is obtained. The value of the time delay in transmission has no relation to the lag synchronization condition, which has been verified by numerical simulations for the original system.