Cull surname in Leitrim

I was wondering if there might be a connection between the Culls from Leitrim and Down. My ancestors are from Clonallon or Kilbroney Parish in County Down. Most Culls come from this area, as well as Kilkeel. I know that during the 1790s, especially after the Battle of the Diamond, many families from Armagh and Down fled to Leitrim, among other parts of Connacht. There's a monument to them in Ballinamore, Leitrim. Does anyone know the history of the Culls in Leitrim? Do they pre-date these events?