Computing the overall reliability of lifeline systems requires studying the changes in target operational objectives, such as connectivity loss and flow reduction, for all possible failure scenarios. Even for simple cases with sparse network topologies where the state of every node and link is binary, this approach involves a combinatorial analysis that leads to an NP-hard computational problem. This paper presents a topology-based method that provides a lower and upper bound to the reliability estimation of networked systems. The size of network failure sets is investigated for several ideal infrastructures, which range from minimally connected radial topologies, to enhanced mesh-like topologies. Sensibility analyses are conducted across different topological layouts and multiple system-level operational criteria. Results show that clustered reliability relationships emerge as signatures for distinct lifeline topological configurations. This observation allows for customized reliability assessment of infrastructure systems that minimize the computational complexity and provides insights into the effects of topology on network performance.