Hello Shelley, I understand that your Buxton Lawn may have connections to east Norfolk, England. I have Lawn ancestors in that area: William LAWN was born c.1756. He married Ann PORTER. Their Halvergate children included: John LAWN 1789, Easter LAWN 1800, William LAWN bp1804. William (senior) died at Halvergate in 1846.
William LAWN (junior) was baptised 1804 at Halvergate in 1804. He married an Elizabeth, and they had at least 5 children: William LAWN c.1836, Maryanne LAWN c1838, Betsy LAWN c.1849, Eliza LAWN p1849, and John LAWN 1851.
Eliza LAWN was born in 1849 at Tunstall, she married George Tammas-Tovell at Tunstall in 1866, and died at Halvergate in 1941. One of their children was Sam Tammas-Tovell - my great grandfather.
The Lawns, like most, were agricultural labourer families, although William Lawn (1804) was unusual, in that he must have been literate. His headstone records that he served as a parish clerk for 33 years.
Lawn is not a common name in the area, and if your Buxton did come from Norton Subcourse, only a few miles away, I should imagine that there must be a very good chance of connection, keep in touch!