The Lok will meet either holders Shotts Bon Accord or Benburb at Newlandsfield tomorrow week – if that tie goes ahead at Hannah Park tomorrow.
Richardson will also have the added advantage of being able to send someone to watch both sides when they do get together.
Glasgow city's other surviving representative, Shettleston, were given an added incentive for tomorrow's replay with Irvine Meadow in knowing that a victory over the Ayrshire cracks will ensure a home tie against Cumnock.
Full draw: Pollok v Shotts or Benburb, Blackburn Utd or Glencairn v Pumpherston or Musselburgh, Lochee Utd or Ardeer v Auchinleck, Rob Roy or Rosyth FC v Dundee Violet or Bo'ness, Johnstone Burgh or Dundonald Bluebell v Camelon, Kelty v Kinnoull or Kilsyth, Shettleston or Irvine Meadow v Cumnock, Linlithgow v Jeanfield Swifts or Montrose Roselea. Ties on Saturday, February 16 (2pm).