It was almost three consecutive losses on Gameweek 3 against Nottingham Forest when Brennan Johnson gave them an 81st-minute lead but Demarai Gray's goal in the 88th-minute salvaged a point at Goodison Park.
Brentford, on the other hand, have had a respectable start despite last weekend's 3-2 last-minute defeat to rivals Fulham. Four points have been secured from the opening three matches, including a win against Manchester United, and the Bees have been prolific in front of goal scoring eight.
Thomas Frank's side did the league double over the Toffees last season with a 1-0 win at home and an impressive 3-2 win in Merseyside that saw Brentford overturn a 2-1 deficit and Everton have two men sent off.
This weekend's visitors did manage to secure their first win against Brentford since February 1954 with a 4-1 FA Cup win in February in what was Lampard's first game in charge - It is worth noting that the two teams had only met twice since then.
The two teams were in Carabao Cup action this week and both secured progression to the third round. Brentford won 2-0 away to Colchester United while Everton got a narrow win away to League One Fleetwood Town.
There are no new absentees for Thomas Frank. Kristoffer Ajer has returned to training after undergoing hamstring surgery earlier in the summer as has Sergi Canós while Ethan Pinnock (knee) continues to recover.
Mikkel Damsgaard made his debut against Colchester during the week and could return to the squad after missing out against Fulham last weekend.
The Toffees will be without a number of key players for this fixture.
Ben Godfrey is a long-term absentee after fracturing his fibula in their opening game of the season; Dominic Calvert-Lewin and Abdoulaye Doucoure, who are both expected to return next month, miss out due to knee injuries.
Raya; Roerslev, Jansson, Mee; Hickey, Nørgaard, Janelt, Henry; Mbeumo, Toney, Lewis-Potter.
Pickford; Holgate, Coady, Tarkowski; Patterson, Onana, Iwobi, Mykolenko; McNeil, Rondón, Gray.
Brentford: Keane Lewis-Potter
The 21-year-old has had to make do with two sub appearances and a cup start since his club-record fee move from Hull City, but in those he has shown great promise and could be in contention to start this weekend.
He made an impression off the bench against Leicester City and Fulham, helping to recover a two-goal deficit as his directness, speed, trickiness on the ball, tenacity and willingness to get in behind made it difficult for the opposition to contend with.
Lewis-Potter made his first start in the Carabao Cup against Colchester on Tuesday and scored his maiden goal with a composed one-on-one finish. While it is not guaranteed that he will start and if he doesn't, then he will make an impact off the bench if called upon.
Everton: Demarai Gray
Gray will be on a mission to do something he is yet to do in his career: score against Brentford.
Having faced them seven times across his time at Everton, Leicester, and Birmingham City, the Bees have managed to keep him quiet, with him only registering one assist - that coming in Everton's 4-1 FA Cup win.
He comes into this fixture in good form having scored in his last two appearances and is Everton's top scorer so far, albeit the only scorer.
The 26-year-old is well-known in the league as a tricky winger and given Aaron Hickey and Rico Henry's tendencies to push forward together with Pontus Jansson and Ben Mee's lack of pace, Gray could have a lot of space to use of and will be the one to cause Brentford problems, in particular if Anthony Gordon is to miss out.
Where is the game being played?
What time is kick-off?
The kick-off is at 15:00 (BST) on Saturday, 27 August.
How to watch?
This game is not being broadcasted in the United Kingdom.