We propose a framework to manage the link lifetime in an IP backbone network by exploiting the sleep mode (SM). In particular, when an SM feature is available, two different effects coexist: during the SM state, the lifetime tends to be increased and however, when the link changes its power state (from SM to full power or vice-versa), the lifetime tends to be decreased. We, therefore, define an optimal formulation of the lifetime-aware network problem. Moreover, we propose a heuristic, called Acceleration Factor Algorithm, to practically manage the device lifetime. We solve the problem both optimally and with our heuristic, considering two representative case studies. Results show that our approach outperforms the previous energy-aware algorithms, which instead do not consider the lifetime decrease triggered by the power state change. Thus, we argue that a lifetime-aware network management should be pursued when deciding to set an SM state for each device in an Internet Service Provider network.