Directional sensor networks (DSNs) are ad-hoc networks which are utilized in different industrial applications. Their usual engagements are to monitor and to perform the coverage of all specific targets in the observing fields permanently. These kinds of networks include numerous configurable directional sensors in which they can be utilized in one of the possible directions along with the one of their adjustable ranges. Although the energy harvesting methodology is being applied for these battery-hungry applications, the battery management and network lifetime maximization are still prominent challenges. In this paper, the network lifetime extension is formulated to a discrete optimization problem which is a famous non-deterministic polynomial time hardness (NP-Hard) problem. To solve this combinatorial problem, a discrete cuckoo search algorithm (D-CSA) is designed and is called in several rounds. A cover is a sub set of configured sensors capable of monitoring all targets in the observing field. In each round, the most efficient cover is constituted along with its activation time. In the determined activation time, the sensors in the cover are scheduled in wakeup mode whereas others are set in sleep mode to save energy. Despite other meta-heuristic algorithms, this proposed algorithm utilizes the novel defined discrete walking around procedures that makes to reach a good balance between exploration and exploitation in this complex search space. The proposed algorithm has been tested in different scenarios to be evaluated. The simulation results in the variety circumstances prove the superiority of the proposed algorithm is about 20.29%, 19.55%, 14.40%, 14.51%, 7.70% and 8.03% in term of average lifespan improvement against H-MNLAR, Hm-LifMax-BC, GA, ACOSC, H-GATS, and HDPSO algorithms, respectively. The results also show the high potential scalability of the proposed algorithm.