LAWRENCE Migration to Philadelphia?

[HowardRayLawrence]

George Lawrence, Sr., b. 26Mar1757, Ballingrane, Limerick, Ireland, m. SARAH BECHRAFT BEACROFT BEACRAFT, baptized, 31 Mar 1759, Ballingrane, Limerick, Ireland, d. 5Aug1848, Virgil, aka Lawrenceville, near Niagara.

His parents are Peter (Laurence) Lawrence, Sr., b. 1704, Killiheen, Limerick, Ireland, m. Agnes Benner, Killiheen, Limerick, Ireland, d. 1763, Killiheen, Limerick, Ireland.

Agnes Benner remarried to Peter Miller in 7 OCT 1765 at Rathkeale, Courtmatress, Limerick, Ireland.  They immigrated to Philadelphia with her children, Elizabeth and George. 1766. (According to Eula Lapp, Agnes Benner's migration with Peter Miller occurred in 1768.)

They joined The Camden Colony of Methodists in New York. At the time of The American Revolution, they became United Empire Loyalists.  They resettled in St. Armand, Quebec. George became a Loyalist Captain in Butler's Rangers, Fort Niagara, and The War of 1812. He was founder of Lawrenceville, aka Virgil; and he was a Methodist teacher, known as a "saint", or saintly man.

What is the correct date, place, and ship of the immigration?