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In this paper, we focus on minimum cost routing in the Wireless Sensor Networks (WSNs). In-network data is often routed in such a way that it can minimize overall energy consumption or it can maximize the network lifetime. However, these metrics do not take into account other costs such as queueing delay and congestion. We solve the problem by introducing a comprehensive cost function and formulating the problem as minimizing the overall cost with a lifetime guarantee. We demonstrate the convexity of the problem and introduce Lagrangian Duality method to decompose the problem. A gradient projection based algorithm is proposed to solve the problem in a fully distributed way. The convergence of the algorithm is verified theoretically. We show through extensive numerical results that our proposed algorithm converges quickly to the optimal solution, and that our algorithm has a better performance than existing algorithms.