Final answer:
George Whitefield, associated with the Wesleys and the Holy Club at Oxford, was a significant figure in the Great Awakening and was the young lay preacher who advocated for lay preaching, which influenced John Wesley's views.
Step-by-step explanation:
The young lay preacher who convinced John Wesley that laymen should be permitted to preach was George Whitefield. Whitefield was a student at Oxford who joined the Holy Club, inspired by the Wesleys and their methodical approach to religion which led to the founding of Methodism. However, it was Calvinist ideals and the influential writings of Jonathan Edwards that converted Whitefield. His belief that the Holy Spirit could be felt at work in the hearts of the faithful drove him to preach emotional and impassioned revivals, reaching out to those beyond the traditional Anglican Church. It was within this context of revivalism and preaching that Whitefield's advocacy for lay preaching gained substantial influence, contributing to a more fervent and expansive method of spreading religious beliefs. This was part of a larger religious awakening happening during that period known as the Great Awakening, affecting both Europe and the American colonies.