Modern creation, possibly meaning The Brian or noble
Labrian is a modern American invention, likely created by combining the French-influenced prefix 'La-' with the traditional Irish name Brian. As Brian is derived from an Old Celtic word meaning high or noble, Labrian is often interpreted with similar connotations of strength and status.
Less common today
Labrian isn't in the latest US Top 1000. It last peaked at #7,772 in 1991.
US births per 5-year period, 1990βpresent (SSA data).