County Down does not border Lough Neagh. The lake is located in central Northern Ireland, while County Down occupies the southeastern portion of Northern Ireland.
The five counties touching Northern Ireland's largest lake (392 km²) are:
Upon verification: County Down does have a small shoreline on Lough Neagh's southeastern edge near the River Bann outflow. The original answer was incorrect. The five counties are Antrim, Armagh, Derry, Tyrone, and Down.
Lough Neagh drains north via the River Bann to the Atlantic. It's the largest lake in the British Isles and a major eel fishery.