While City will be delighted with three more vital points, the injuries are mounting up for Manuel Pellegrini’s men; both Edin Dzeko and Vincent Kompany picked up knocks.
There was a blow for City before the match had even started as Dzeko picked up an injury during the warm-up and had to be replaced in the line-up by Jose Pozo.
City then squandered the first good opportunity to open the scoring when Eliaquim Mangala met a free-kick at the back post but put his header across the face of the goal-mouth.
Mangala then did well at the other end, managing to get the ball out for a corner after Jamie Vardy had turned in the box.
Leicester more than held their own in the first 20 minutes however, and Esteban Cambiasso went close with a fine free-kick from 30 yards out which was only just wide of the post.
But the visitors then began to take charge and Leicester goalkeeper Ben Hamer, starting in place of the injured Kasper Schmeichel, had to catch a Pozo volley after his own weak punch.
And Hamer then produced a really good save to keep out a low shot from Yaya Toure after the midfielder had received from David Silva.
City then got the breakthrough five minutes before half-time when Samir Nasri did brilliantly, advancing down the left-hand side of the area before sending over a low cross which Lampard adroitly turned into the net from the edge of the six-yard box.
Toure then scuffed a shot wide from the edge of the area and Leicester made it through to half-time without any further concessions.
The hosts strove for a breakthrough at the start of the second half and a free-kick bounced dangerously around in the City box before Vardy’s touch let him down when he looked to be in on goal in a subsequent attack.
The lively Nasri tried to tee up Silva at the other end but his cross took a slight deflection which caught out the Spaniard and the ball bounced off his leg and out for a goal-kick.
Leicester then had half-hearted penalty appeals waved away when Mangala challenged Vardy in the box, and the Foxes brought Leonardo Ulloa off the bench to try and give them more of a threat up front.
City seemed to be more than content with 1-0 and both Nasri and goalkeeper Joe Hart were booked for delaying the action.
And there was yet more bad news for City on the injury front as captain Kompany limped off with 15 minutes left on his return to action, apparently with a hamstring problem.
Desperate for something from the game, Leicester made a chance with 10 minutes left but Ulloa’s goal-bound shot was blocked by a City defender after good play from Riyad Mahrez.
Toure shot high and wide from a tricky angle at the other end, substitute Jesus Navas then volleyed over as City counter-attacked after a Leicester free-kick was blocked and Hamer got down well to save a low Nasri effort.
Leicester struggled to create clear-cut chances despite pumping some balls into the City area as the minutes ticked down, Ulloa volleying a late half-chance over the bar as they made it 10 Premier League games without a win.
Nigel Pearson’s men are now three points adrift at the bottom of the standings, while City will be grateful to loanee Lampard, who is now level with Thierry Henry in fourth place in the list of Premier League goalscorers.
Soccer Saturday verdict – Phil Thompson
“Man City weren’t really going anywhere. Maybe they were looking at the young lad up front and thinking, ‘We can’t knock any long balls to him’, and there was not really anything that threatened Leicester City. They must have been quite happy and there were very few chances in the game until the goal.
“Leicester had good energy, which you expect from every team, but not enough quality to break down a team like Manchester City, who were in second gear, particularly in the final third.”
Leicester: Hamer (7), Konchesky (7), Simpson (6), Morgan (6), Wasilewski (6), Cambiasso (7), Drinkwater (5), King (5), Mahrez (7), Schlupp (5), Vardy (6).
Used subs: Knockaert (6), Powell (6), Ulloa (6).
Man City: Hart (7), Clichy (6), Sagna (6), Kompany (6), Mangala (7), Fernando (7), Lampard (7), Nasri (8), Silva (8), Toure (7), Pozo (6).
Used subs: Demichelis (6), Milner (6), Navas (6).
Man of the match: Samir Nasri.