I have a book "Memories and Records of Eastern North Carolina" by Mary Weeks Lambeth; 1957.The author has quite a few pages on the Lambeth family.A couple of items might be of interest to you:
"Letter from China by James William Lambuth dated Shanghai, China, Feb 12, 1884 - My great grandfather dame from England and settled in VA.His name was orig. Lambeth but during the Rev. War he had it changed to Lambuth.My grand fa. Rev. Wm. Lambuth was born in Hanover County, VA, near Hanover Court House in 1765.He received license to preach at age of 21 and became a member of Baltimore Conf.He travelled i the Conf. for several years was ordained Deacon by Bishop Coke, elder by Bishop Asbury.In 1798 he was send to wilds of Tenn. as a missionary, was married to Miss Creenhaw (Greenhaw), settled first in Smith Co., and afterwards moved to Summer Co., in a mile of Fountain Head where he lived to his death in 1837.He was known as 'old father Lambuth, the comb-maker.'His death was peaceful, pasing away, as one falling asleep.He was buried in the Fountain Head cemetery."
"My Father, Rev. John Russell Lambuth, was born in Sumner Co., Tenn., in 1801....In 1817 at the age of 16 he was licensed to preach and joined the Tenn. Conf. which met at Fountain Head in that year...My father was at once appointed as missionary to the creoles of LA. and to the Indians."
That is part of the letter.The next chapter entitled "Lambuth - Rev. William Lambuth evidently came to Tennessee as his son, Rev. John Russell Lambuth was born in Sumner County, Tennessee, August 12, 1801.Rev. John Russell Lambuth served the Methodist Church in Greene County, Alabama and possibly other places.His son Rev. James William Lambuth was born in Greene County, Ala. March 2, 1830."
There are quite a few 'Johns' listed in the book, but the only Meredith was "Wm. M. Lambeth of New Orleans and sister Frances Bernard Pitts were evidently the children of John and grandchildren of Meredith Lambeth and Frances Bernard formerly of King Wm. County"(prob. VA)