No, he can't belong to Os because in the 1870 census Os was 6 yrs old and Lawrence was 3. thought he might have been Mary Janes son as she was 21 in 1870. In the 1880 census Lawrence was listed as a grandson of Latons. He was still listed with the family and Mary Jane died in 1877. I can't find any other mention of Lawrence anywhere.
Here are the dates I have Laton abt 1825, Caroline abt 1821
Mary Jane 6/7/1848-7/14/1877, Lucille 5/10/1849-9/8/1932, Ambros Fagan my greatgrandfather 6/9/1850-7/9/1933, James Wesley 4/1856-7/31/1923, Amarynth (Addie)6/5/1860-11/25/1934, Osborne Obadiah 7/24/1863-3/31/1940. Any more info on Laton or Caroline would be greatly appreciated. I have a copy of their marriage license wed 7/27/1847 Caldwell co. N.C. thanks Walt Martin