The Red Imps were second best for much of the game but were saved from defeat by a spectacular equaliser by Sam Mullarkey.
Adrian Patulea had an early chance for Lincoln but his shot from outside the box was saved at full stretch by Kevin Pilkington.
But County were still in control with Matt Hamshaw and Myles Weston both going close with shots.
Then Jamie Forrester, playing against his old club, set up a chance for Hamshaw in the 33rd minute but the midfielder was off-target.
Five minutes later Weston comprehensively beat Lee Beevers down the left and sent in a low cross which was blocked by Moses Swaibu.
The ball came back to Notts skipper John Thompson but his goal-bound shot was kept out by Janos Kovacs' desperate clearance.
County went close again a minute before half-time when Phil Picken played a perfect ball into the area for Forrester. The striker turned and fired in a shot which Rob Burch did well to push over.
Forrester had another chance in the 62nd minute following good work by Weston. The winger fired in a low cross which ended up with Forrester on the far post but Lincoln keeper Burch saved.
The game came to life in the 64th minute when a mix-up between Lincoln centre-back Swaibu and keeper Burch left Delroy Facey in the clear. The striker steadied himself and sent his shot low into the empty net.
But the lead lasted just 30 seconds with Lincoln levelling almost straight from the restart.
Mullarkey won possession 25 yards out and hit a left-foot shot into the top corner that gave Pilkington no chance.
Lincoln could have won it three minutes later when a cross from Aaron Brown found Patulea inside the six-yard box but the striker lost his footing in front of goal and the chance was lost.