In our Witter family, I have one Witter who was in Lancashire, namely, John Witter (born 1774 Christleton, died 1850 Toxteth, Lancs.), son of John Witter (1745-1792) [son of John Witter (1720-1768) and Mary Richardson (1718-1798)] and Elizabeth Roberts (1755-1820).
However, there may have been other grandchildren of John Witter (1720-1768) who ended up in Lancashire, possibly through sons Richard (1753-1820) or Samuel (1750-?).
~Jamie Reid