This paper studies the problem of how to maximize the network lifetime while preserving network coverage for an energy constrained wireless sensor network. We consider network coverage from an our recently proposed information coverage model [1] other than the conventional sensing disk model. The lifetime maximization problem is modeled as a nonlinear programming problem and is shown NP-Complete. We then propose a family of greedy algorithms to allocate sensors different roles such that different sensors may consume different amount of energies in different intervals to prolong network lifetime while still guaranteeing application requirements. Simulation results suggest that the algorithm with the best balancing between communication energy consumption and area coverage requirement has the highest network lifetime.