City put in a performance of real spirit at Leyton Orient but came away without the point their battling display deserved.
The Imps trailed thanks to two Sonny Perkins strikes after a frustrating first half, but the fightback was started by Lewis Montsma just before the interval before James Collins completed the comeback.
City looked set to claim at least a point, but were undone in time added on at the end of the match when Charlie Kelman snatched a winner for the hosts who showed why they are the form team in the division.
Sam Clucas was handed his first Imps start since returning to the club in January - 5,617 days after his last appearance for City. The 34-year-old midfielder had previously only featured in one Johnstone's Paint Trophy game against Darlington on September 1 2009.
Lewis Montsma, Dom Jefferies, Jovon Makama and Ben House also came into the starting XI. Tendayi Darikwa was left out of the squad having become a father again.
The home side started confidently as you would expect from the division's form side, but they were well marshalled in the opening stages of the game. Charlie Kelman lifted an effort wide after three minutes, but otherwise Orient's neat play in the middle of the pitch did not lead to chances.
City relied on their frontline to work hard and stretch the game, with Freddie Draper, Jovon Makama and Ben House all pressing high .
The Imps threatened after 12 minutes when Clucas found the run of House, but the assistant's flag was up to prevent him turning and getting a shot away.
The Imps thought they had seen out the early threat, but the home side went ahead through a well-worked free-kick after 18 minutes which led to Sonny Perkins heading home.
Paudie O'Connor thought he had levelled shortly afterwards when he turned the ball home from House's pull back, only for the assistant's flag to go up.
City's gameplan was proving effective in terms of chances created, with it needing a perfectly-timed header from Jack Simpson to stop Makama turning in Sean Roughan's cross.
The home side doubled their lead after 28 minutes, with Galbraith doing brilliantly before playing in Perkins who fired home his second of the match.
Orient's clinical finishing had given them a 2-0 lead. In a game of fine margins, the Imps were just not getting the rub of the green - with a second goal ruled out on the half-hour mark as House headed in from Draper's cross. For the second time in the match, the assistant's flag went up to rule out a City goal.
And, after 35 minutes, the fine margins again went against the visitors after high pressing up the home defence led to a short clearance from home keeper Josh Keeley falling to Clucas. The midfielder tried to lift the ball into the far top corner, only to see the ball land just over the bar.
Kelman and Tom James tried efforts from distance which flashed just wide for the hosts, but it was the Imps who got the third goal to get back into the game.
Hackett's delivery from the left found O'Connor whose flicked effort was only just clawed out by Keeley. O'Connor was questioning whether the ball had crossed the line, but Monstma was in no mood to wait as he fired home on the rebound to half the deficit right before the interval. This time there was no hint of an offside flag to ruin the moment.
The opening spells of the second half were scrappier, with City effectively stopping Orient from playing their passing game.
City's first clear chance of the half came after 58 minutes, and it was made by Makama who won the ball on the right before crossing. Hackett collected the ball, via a deflection, and fired towards the near low corner - but Keeley did well to save with his legs.
With the game entering the final 30 minutes there was no sign of the Imps giving up on a way back into the game, with James Collins sent on in place of Draper.
Makama went close after 66 minutes after he got on the end of a Hackett cross, after a good move. Moments later it took another great header from Simpson to prevent Hackett's left-wing cross finding one of three Imps players who were lining up in the box to attack the ball.
Orient head coach Richie Wellens made changes of his own as he tried to regain control of the match, with an effort from Jordan Brown which went wide the best his side had to show for the second half at that stage.
The equalising goal came after 75 minutes. Tom Bayliss' first touch after replacing Clucas was to take a free-kick from wide on the left. He found O'Connor whose header was kept out by a scrambling Keeley, but Collins showed his striker's instincts to turn the ball home.
City pushed for a winning goal, but in the end were hit by a sucker punch when Dan Agyei's cross fell for Kelman who fired home.
Imps: Jeacock, Montsma, Hackett, McGrandles, O'Connor (c), Jefferies, House (Hamilton, 89), Roughan, Clucas (Bayliss, 75), Makama, Draper (Collins, 60). Sub not used: Wickens, Jackson, Ring, Collins, Okoro.
Orient: Keeley, James (Cooper, 45+3 (Jaiyesimi, 82)), Simpson, Brown, Williams (Donley, 67), Currie, Perkins (Ball, 67), Galbraith, Kelman, Edmonds-Green, Aboudai (Agyei, 82). Subs not used: Phillips, Markanory.
Referee: Matt Corlett
Attendance: 7,967 (793 away)
