Managerless Lincoln could only manage a goalless draw with Barrow in the Blue Square Bet Premier.
David Holdsworth left the Imps by mutual consent last Sunday following a run of one victory in 10 games.
Danny M Rowe went close for the Bluebirds only to be denied by Paul Farman, while Alan Power fired straight at Danny Hurst.
Farman denied Richie Baker, Alex-Ray Harvey and Danny L Rowe, while Colin Larkin forced Hurst into action again.
Lincoln are just three points ahead of 22nd-placed Barrow having played one game more.