I'm assuming the name is feminine and African American and is pronounced la-SAHN-ya/la-SAWN-ya. (Though please correct me if this is wrong.)
If so, it could be a variant of Lasonya, a combination of the popular prefix La- (found in names like
Latisha and
Latonya) and the name
Sonya.
Lasonya briefly charted in the early 1970s:
http://www.behindthename.com/top/search.php?terms=lasonyaThis message was edited 5/8/2013, 4:10 PM