The hosts made a vibrant start to the match and deserved the lead when Mason Mount gave it to them after only seven minutes, but it proved to be a game of two halves at Stamford Bridge.
Leicester looked like an entirely different team after the interval and equalised through Wilfred Ndidi before missing a string of chances to condemn Chelsea to a third consecutive defeat at the start of the campaign.
The result leaves the home side with just one point from their opening two league outings under Lampard, while it is back-to-back draws for Leicester at the start of the new campaign.
Lampard's reign had begun in disappointing fashion with defeats to Manchester United and Liverpool, but his Stamford Bridge bow got off to a flying start and Chelsea could have taken the lead inside the opening minute when Olivier Giroud knocked the ball into the path of Pedro, who lashed his half-volley into the side-netting.
It was an early warning sign for Leicester as Chelsea refused to let up in the opening exchanges, with Mount then being denied by Kasper Schmeichel moments later and Christian Pulisic unable to bundle the rebound home.
The early breakthrough did come after seven minutes as the lively Mount marked his home Chelsea debut with a goal, stealing possession off a languid Ndidi before slotting his finish into the bottom corner despite being off balance.
The hosts did take their foot off the pedal after the opener, but they still looked by far the more likely to score another and Mount almost doubled his personal tally after 21 minutes when his unmarked header was straight at Schmeichel.
Giroud - chosen ahead of Tammy Abraham to lead the line - was proving to be a particular pain for the Leicester defence with his link-up play and his delightful flick almost created a second five minutes later, only for N'Golo Kante to be denied by a fine last-ditch challenge from Christian Fuchs.
Leicester offered precious little during a half in which they were comfortably second best, although they were almost gifted an equaliser when Kepa Arrizabalaga was close to being closed down by Jamie Vardy.
The visitors were at least able to stunt Chelsea's dominance as the first half wore on, and that continued in the early stages of the second half too as they looked to undo the damage from their sluggish start.
There were still sights of goal for the hosts, with Giroud drawing a routine save from Schmeichel, but Leicester were offering more in reply and forced Kepa into action through Hamza Choudhury's long-range effort shortly before the hour mark.
Youri Tielemans then fired off target before Leicester's improvement was rewarded with the equalising goal, and it came via a moment of redemption for Ndidi.
The increasingly-influential James Maddison delivered a pinpoint corner which was met by a thumping header from the Nigerian midfielder, who sent it flashing past Kepa to atone for his earlier error.
Suddenly it was Leicester that looked by far the more likely to go on and get all three points, and Maddison should have put the Foxes ahead with less than 20 minutes remaining when he dribbled into the box only to blaze his effort over when he would have expected to score.
Having escaped unscathed from that scare, Chelsea were then thankful for some errant finishing again shortly afterwards when Vardy flashed a low strike across the face of goal after being played through by Maddison.
The desire of both teams to win the match made for an open end to the game, but as was the case for the entirety of the second half it was Leicester who came closest to scoring when Tielemans was denied by Kepa in the 89th minute.
Chelsea could only respond with wasteful and wayward long-range shots from Kurt Zouma and Abraham as they picked up a solitary point which lifts them up to 15th, but leaves them already five points adrift of early pace-setters Liverpool.
Lampard is now the first Chelsea boss to fail to win any of his first three games in charge of the club since Rafael Benitez in 2012-13 and the first to fail to win his first home league game since Avram Grant in 2007.
CHELSEA (4-2-3-1): Kepa; Azpilicueta, Christensen, Zouma, Emerson; Kante, Jorginho (Kovacic 71'); Pedro, Mount, Pulisic (Willian 71'); Giroud (Abraham 61')
LEICESTER (4-5-1): Schmeichel; Pereira, Evans, Soyuncu, Fuchs; Perez (Albrighton 80'), Tielemans, Ndidi, Choudhury (Praet 73'), Maddison; Vardy