The result plunged the Toffees into the relegation zone after Burnley had won 1-0 against Wolves earlier in the day.
With the Whites' next three games against Manchester City, Arsenal and Chelsea, Jesse Marsch will be keen to see his side pick up something in the capital tonight.
Leeds would have been slightly relieved to see Andrew Robertson and Divock Origi net goals at Anfield, after Everton had successfully frustrated their title-chasing hosts for an hour.
According to the The PA news agency, Everton are unhappy that a second-half incident involving their forward Anthony Gordon, who had previously been booked for diving, and Liverpool defender Joel Matip was not given due consideration.
Referee Stuart Attwell decided no penalty should be awarded and VAR did not intervene as the game continued at 0-0.
Lampard said after the game he felt it should have been a spot-kick and claimed it would have been given at the other end for Liverpool if a foul had occurred on Mo Salah. The Egyptian has been awarded four free-kicks in his last 908 minutes of Premier League football.
However, the consensus within Everton is the same as Lampard's view. Matip's challenge on Gordon, which occurred with the game at 0-0, could have changed the course of the game if the officials decided to award a penalty.
Last month the club received an apology, following another official complaint, from PGMOL chief Mike Riley following the failure to award a handball against Rodri in the home defeat to Manchester City.
On that occasion referee Paul Tierney was unsighted and the VAR, Chris Kavanagh, decided there was insufficient evidence to show the ball had hit the City midfielder on the arm despite television replays being fairly conclusive.