Lockdowns are disease mitigation strategies that aim to contain the spread of an infection by restricting the interactions of its carriers. Lockdowns can thus have a considerable economic cost, which makes the identification of optimal lockdown windows that minimize both infection spread and economic disruption imperative. A well-known feature of complex dynamical systems is their sensitivity to the timing of external inputs. Hence, we hypothesized that the timing and duration of lockdowns should dictate lockdown outcomes. We demonstrate this concept computationally from two perspectives - Firstly, a stochastic "small-scale" Agent Based Model (ABM) of a Susceptible-Infected-Recovered (SIR) disease spread and secondly, a deterministic "large-scale" perspective using a multi-group SIR mass model with parameters determined from the SARS-CoV2 data in India. Lockdowns were implemented as an effective reduction of interaction probabilities in both models. This allowed us to evaluate the parametric variations of lockdown intensity and duration onto the dynamical properties of the infection spread over different connection topologies. We definitively show that the lockdown outcomes in both the stochastic small-scale and deterministic large-scale perspectives depend sensitively on the timing of its imposition and that it is possible to minimize lockdown duration while limiting case loads to numbers below hospitalization thresholds.