Lampard's last game in charge was Saturday's 2-0 league defeat at West Ham United, which kept Everton second-bottom of the table on 15 points after 20 games, above Southampton on goal difference, and two points adrift of the safety zone.
John Lundstram struck 10 minutes from time to give Rangers a 3-1 win over RB Leipzig and send them into the final 3-2 on aggregate after a see-saw clash at a rocking Ibrox.
Atalanta goalkeeper Juan Musso saved a penalty and a follow-up attempt but he couldn't keep out an own-goal by Davide Zappacosta from the resulting corner as Leipzig salvaged a 1-1 draw.
Arsenal's third successive league win lifted them above West Ham United into fifth place with 45 points, one behind Manchester United but having played two fewer games.
Minamino came off the bench to score in a 3-0 win for Jurgen Klopp's side.
The Hammers moved within a point of fourth-placed Arsenal.
West Ham came from behind twice and then claimed all three points with a late goal from substitute defender Arthur Masuaku.
The win lifts City back up to second place on 29 points.
Victory for high-flying West Ham lifted them above Juergen Klopp's side into third place in the table.
Cristiano Ronaldo scored his fourth goal in three games.