The Red Imps, without a win in their previous six games, produced a much-improved performance. They deservedly went in front but then lost their momentum after conceding a soft own-goal and had to settle for a point.
A four-man move set up Louis Dodds in the sixth minute but his shot from the edge of the box was pushed away by Morecambe keeper Joe Lewis.
Lincoln kept up the pressure and, after Scott Kerr had had a shot charged down by David Artell, keeper Lewis was forced to save to keep out a header from Steve Torpey.
Morecambe quickly hit back with Gary Thompson putting Michael Twiss in the clear, but the striker fired his shot into the side-netting.
The Shrimps had a chance to go in front on 20 minutes when Lincoln failed to clear a free-kick from Adam Yates. The ball fell to Carl Baker, unmarked at the far post, but his low shot was blocked by the legs of Lincoln keeper Alan Marriott.
Lincoln quickly pushed forward and went in front in the 22nd minute. Oliver Ryan's neat pass sent Ryan Amoo into the box and the defender blasted his shot into the roof of the net giving Lewis no chance at all.
Ryan had a good chance to increase Lincoln's lead ten minutes later but saw his close-range shot blocked by Lewis.
However, a horrendous defensive mistake allowed Morecambe to level in the 36th minute.
Baker's deep cross to the left was headed into the six-yard box by Thompson. No Morecambe player was near enough to trouble the Lincoln defence but City's Lee Beevers did the job for them - stabbing the ball into his own net.
Baker could have won the game for the Shrimps when another mistake allowed him to break free, but his shot from the edge of the box was saved by Marriott.