Livingston have been drawn away from home to League One side Forfar Athletic in the last-16 of the Betfred Cup.
The game will be played on August 17 or 18 with a spot in the quarter-finals up for grabs.
The Lions booked their place in the second round after a penalty shoot-out victory over Falkirk was followed by wins over Ayr United, Stranraer and Berwick Rangers in Group G.
Last season, Livi suffered a 1-0 loss at home to Motherwell in the second round in what would prove to be Kenny Miller's last game as manager.
Full draw: Hibernian v Greenock Morton, Partick Thistle v Ross County, Motherwell v Heart of Midlothian, Dundee v Aberdeen, Celtic v Dunfermline Athletic, Forfar Athletic v Livingston, Kilmarnock v Hamilton Academical, East Fife v Rangers.
