The son of Roger Laurence, armorer, he was born 18 March 1670, and admitted on the royal mathematical foundation to Christ's Hospital in April 1679, from the ward of St Botolph, Bishopsgate, on the presentation of Sir John Laurence, merchant, of London.
It was discussed at a dinner of thirteen bishops at Lambeth Palace on 22 April 1712, and a declaration was drawn up in favour of the validity of baptisms performed by non-episcopally ordained ministers.
Through the influence of Charles Wheatly, then Fellow of St John's College, Oxford an honorary degree of M.A.
He was ordained deacon on 30 November, and priest on 19 December 1714, by the nonjuring bishop George Hickes.
In 1716–18 nonjuring ordinations took place in Lawrence's chapel on College Hill, City of London.