Thrashed 4-0 at Manchester United last weekend and beaten on penalties by Liverpool in the European Super Cup on Wednesday, Lampard's side took an early lead through Mason Mount's first goal for Chelsea.
But Ndidi atoned for the costly mistake that led to Mount's opener as the Nigeria midfielder headed Leicester's well deserved second half equaliser.
Lampard had been given a thunderous reception in his first game as Chelsea manager at Stamford Bridge.
Yet the mood was far gloomier by the final whistle after a spluttering display raised the spectre of a potentially difficult season for the returning hero.
Lampard, Chelsea's all-time record goalscorer, managed to avoid being the first Blues boss to lose his first two Premier League games in charge since Gianluca Vialli 21 years ago.
But on this evidence there is a lot of work for the 41-year-old to do if he is to emulate his 13-year playing spell at Chelsea, which included three Premier League titles and the club's first Champions League crown.
Greeted by a huge flag with the message 'Frank Lampard's blue and white army' and another reading 'Welcome home Super Frank', the former England midfielder emerged from the tunnel to cheers and turned to applaud the crowd as they chanted 'Super Frankie Lampard'.
With his former Chelsea team-mate John Terry in the stands to support his old friend, the Blues nearly gave Lampard a dream start in the first minute when Olivier Giroud chested Cesar Azpilicueta's pass to Pedro and the Spaniard volleyed into the side-netting.
Moments later, Mount threatened when he burst through, but the youngster shot too close to Kasper Schmeichel, who did well to block Christian Pulisic's attempt from the rebound.
Mount, a tenacious attacking midfielder in Lampard's mold, didn't need to rue that miss for long.
The 20-year-old, who impressed while playing for Lampard on loan at second tier Derby last season, opened his Chelsea account in the seventh minute, with a helping hand from Ndidi.
When Caglar Soyuncu rolled a pass to Ndidi, he dithered on the ball too long and Mount alertly pressured him into conceding possession before sliding a clinical finish past Schmeichel.
It was just reward for a blistering start from Chelsea and Lampard celebrated by punching the air in delight.
Mount should have doubled Chelsea's lead when he headed straight at Schmeichel from Pedro's cross before N'Golo Kante shot wide from Giroud's flick.
But Chelsea couldn't keep up that ferocious pace and their dip gave Leicester a lifeline they should have taken when James Maddison miscued his pass after dancing around Blues keeper Kepa Arrizabalaga early in the second half.
Giroud had started up froRead More