With his side falling against Jurgen Klopp's men, Lampard became the first Chelsea boss to fail to record a win from his first four home matches in 31 years.
Trent Alexander-Arnold and Roberto Firmino gave the visitors a two-goal lead at half-time, and N'Golo Kante's spectacular second-half goal was not enough to change the result as the Blues' poor run at home continued.
Chelsea's afternoon would be made worse as they saw two starting defenders, Emerson and Andreas Christensen, limp off due to injury in the first half.
The Blues have now drawn two and lost two in all competitions at home under Lampard.
Bobby Campbell, who suffered the same fate in 1988, is the only other manager in Chelsea history to not win any of his first four home games in charge.
The pair of defeats means Chelsea have lost consecutive home matches in all competitions for the first time since April 2014, when they lost against Sunderland and Atletico Madrid.
Chelsea's 2019-20 season is now only the second time the club has failed to win any of their first three Premier League home matches, with the previous time coming in the 2001-2 campaign.
A shaky back line has been partly to blame for Chelsea's poor run of form, as the Blues have now conceded 13 times in just six Premier League games.
That total is the worst Chelsea have ever posted in the Premier League, with the last time the Blues started so poorly defensively coming all the way back in 1978-9.
The Blues will be heavily favoured to grab their first home victory of the season on Wednesday as they host League Two side Grimsby Town in the Carabao Cup.
That game will be followed by another home fixture, this time in the Premier League against Brighton on Saturday.