Natural hazard events can lead to large-scale failures in lifeline systems. By enabling a fast recovery of these systems following failure events, one enhances their resilience. However, this resilience also comes at a cost, e.g. if additional reparation crews need to be hired. In this contribution, we present a work towards the identification of a robust recovery strategy that optimizes the trade-off between the downtime and losses on the one hand and the cost for enhancing resilience on the other. We use a simplified model of the network [1] and simulate system failure events [2] based on a stochastic set of natural hazard scenarios. We employ the frameworks described in [3,4] for modelling the system recovery, and identify the relation between recovery costs and the losses associated with system downtimes. Furthermore, we investigate the influence of the interdependence between lifeline systems in identifying the optimal recovery strategy. We illustrate the methodology with an example of interconnected power and water networks exposed to a seismic hazard.