The Imps turned on the style at Bradford City to virtually ensure progression to the knockout stages of the Papa John's Trophy.
Tom Hopper, Hakeeb Adelakun and Anthony Scully scored the goals to seal victory, while young keeper Sam Long kept a clean sheet in only his second competitive appearance.
The Imps opened brightly, with home defender Fiacre Keller having to be alert in just the second minute to cut out Anthony Scully's pass looking for Adelakun.
Adelakun won a corner moments later with a shot from outside the area.
Sam Long, making his second competitive start, was called upon to stop a powerful Alex Gilliead shot after Regan Poole had blocked Andy Cook's effort.
The Imps were probing with every attacking move, with Adelakun's pass looking for Scully just too close to Sam Hornby in the home goal.
Long again showed he was at home in the first-team with a great save to turn another Cook shot wide.
A good spell of pressure led to the opening goal after 12 minutes, with the ball worked out to Cohen Bramall on the left and his inch-perfect cross was powered home by Hopper for his second goal of the season.
Bishop almost had his second of the campaign himself with a great effort which came crashing off the crossbar following a smart one-two with Scully.
But it was 2-0 moments later as the Imps quickly won the ball back and Adelakun cut into the area from the left. A moment of individual brilliance saw him flick the ball inside the two defenders who were blocking him, and he paced round to blast home his first goal since joining the club.
The home side played their part in the match, with Lewis Montsma clearing a Gillead shot off the line shortly before the break.
The Imps started the second period as they had the first, with Bishop sending a low driven shot just wide of a post with Hornby beaten.
The third goal came four minutes after the restart with a smart counter-attacking move started by Montsma's clearance. Lewis Fiorini led the drive into the area, before laying off a perfectly-timed and weighted ball for the run of Scully who lifted home his seventh goal of the season.
Bantams sub Caolan Lavery almost pulled a goal back moments after his introduction, ending a low effort wide which Long calmly watched all the way.
Both sides continued to play in an entertaining and attacking style as the game moved into the final stages, with Kelleher getting in a key interception to block Bramall's cross and Montsma clicking an effort over.
Matthew Foulds also sent an effort wide for the home side after winning the ball back inside the area.