Mason Mount embarrassed Ndidi to score his first Chelsea goal in the seventh minute as the host side started superbly.
But, as in the 4-0 loss at Manchester United seven days ago and the UEFA Super Cup penalty shoot-out defeat to Liverpool in midweek, the Blues were unable to sustain their efforts over the course of the contest.
Ndidi levelled as James Maddison made life increasingly uncomfortable for Chelsea after the interval, meaning Brendan Rodgers's side has started its campaign with back-to-back draws.
Lampard was serenaded on to the touchline in his first home game at the helm and a party atmosphere was almost ramped up inside the first minute – Pedro thumping a volley from Olivier Giroud's knockdown into the side netting.
It was a high-tempo start from the host, with Kasper Schmeichel denying Mount and smothering Christian Pulisic's attempted follow-up.
The opener felt inevitable and Mount pickpocketed a lackadaisical Ndidi to clip into the bottom corner.
Schmeichel was well-positioned to prevent Mount from heading a second before Christian Fuchs made a goal-saving challenge that denied N'Golo Kante.
Leicester grew into the game before the break and Maddison rounded a scrambling Kepa Arrizabalaga before being crowded out five minutes into the second half.
The playmaker twisted past Anders Christensen and hitf a shot across the face of goal as Chelsea struggled to find their earlier momentum.
If not in the same emphatic manner as Chelsea's goal, the equaliser felt like it was coming by the time Ndidi atoned for his earlier error and converted Maddison's 67th-minute corner.
Maddison's dazzling, inventive play merited reward but he lashed wastefully over 17 minutes from time, before playing in Jamie Vardy to shoot wide. The full-time whistle ultimately felt like more of a relief for a Chelsea side exhausted and overrun by that stage.