There is a lengthy Theravādin discussion of this issue in Ledi Sayadaw’s Dhammadīpanī. It’s given in answer to a query about whether the phrase vinayo ca susikkhito in the Mangalasutta implies that the laity should study the monastic Vinaya.
The sayadaw’s view is that though it’s not essential for them to do so, nevertheless it’s desirable, provided that the layperson is not someone “of weak character”, “undeveloped in mind” and given to fault-finding.
However, wise lay persons who want to promote the Buddha’s teachings, and are well versed in their own discipline, do need to learn the monks’ Vinaya. Why? Those who are well-trained in the householder’s discipline become truly good people, so their minds and motives are good. If they are well controlled by the lay person’s discipline, after learning the monks’ Vinaya, they will not use their knowledge unwisely. They will not defile themselves with impure physical, vocal, and mental actions. They will not accumulate evil motives and evil kammas because of this new knowledge. In the Commentary it is mentioned that a wise, learned brahmin, after listening to the monks’ Vinaya rules in detail, developed a clear mind and strong faith in the Saṅgha. He appreciated the power and significance of the monks’ Vinaya as clear understanding had revealed its profundity.
One day a devoted brahmin heard the monks reciting their Vinaya rules. Appreciating the benefits of these numerous rules he entered the Saṅgha. Thus one’s own attitude and motive are crucial to evaluate the knowledge of Vinaya rules and the diverse conduct of monks.