This study addresses the nondimensional analysis of drop-induced shock mitigated using magnetorheological energy absorbers (MREAs) incorporating a time lag. This time lag arises from two sources: (1) the time required to generate magnetic field in the electromagnet once current has been applied and (2) the time required for the particles in the magnetorheological fluid to form chains. To this end, the governing equations of motion for a single degree-of-freedom (SDOF) system using an MREA with a time lag were derived. Based on these equations, nondimensional stroke, velocity, and acceleration of the payload were derived, where the MREA with a time lag was used to control payload deceleration after the impact. It is established that there exists an optimal Bingham number that allows the payload mass to achieve a soft landing, that is, the payload comes to rest after utilizing the available stroke of the MREA. Finally, the shock mitigation performance when using this optimal Bingham number control strategy is analyzed, and the effects of time lag are quantified.