Notes from http://www.stirnet.com/HTML/genie/british/ll/livingston01.htm#dau1 This family is thought to be of Saxon origin, the name being derived from Leofing (son of Leof). One theory is that a Baron de Leving followed Edward Atheling into exile and then he, or his son, came to Scotland with Edward's daughter Margaret when she married King Malcolm Canmore. Normally identified as the first (formally) recorded ancestor of this family, and probably grandson of Baron de Leving, was .. Leving / Livingus (a 1124)
Notes from www.kilsyth.org.uk/history/archivesources/livingston_line.htm> Leving of Levingstoun settled in West Lothian, southwest of Edinburgh during the reign of King Edgar (1097 1107) and is also known to have been there during the reign of King Alexander I (1107 1124) and King David I (1124 1153). His name was recorded in the latinized form 'Levingus' when he presented the church of his manor to the newly founded Abbey of Holyrood in 1128.