Info mainly from: Special Report on Surnames in Ireland: Together with Varieties and Synonymes by Robert E. Matheson
Moira District has these prefixes:
Baun-Lavery also Bawn-Lavery with Baun being the most common. several people are known by thir prefixes: Dan Baun. Baun-Lavery is know in other districts.
Both Lowry and Lavery names descend from O Labhradha, province of Ulster. The "ban" meaning white is "Baun."
Also Richard Mellish: Where can I find: Ulster Folklife 1845 ? And is that date correct? Is Molly Bawn found in --"Some Songs and Ballads in Use in the Province of Ulster, 1845"?