Derby are an ambitious club and can be a great platform for Lampard and co, but the onlooking Chelsea directors may dream of seeing one of the club's greatest players return to manage.
Davide Zappacosta's cross deflected in off Tomori's standing leg as Chelsea took the lead.
Mount and Tomori are both on loan from Chelsea and Zola enjoyed the duo's performances.
On-loan midfielder Mount was one of the Championship side's most impressive performers, creating the second goal for Martyn Waghorn and going close to scoring. The game nearly went to penalties, with Derby striker David Nugent hitting the post in the final minutes.
Head coach Maurizio Sarri said after that match that Hazard's fitness remains of critical importance, and Zola said that he is on track to return to the team when Crystal Palace visit Stamford Bridge on Sunday.
Chelsea are through to the last eight of the Carabao Cup but only after an action-packed win against Derby County at Stamford Bridge. "This is probably the complaint, but we will go through this and discuss this [with them]".
There were more errors and a few signs of promise from Tomori who was good on the ball and strong in the tackle but perhaps a little too eager to impress after that early blunder, often rushing into areas that left his more experienced - and slow - centre-back partner Keogh exposed.
Lampard received a warm welcome from the home supporters as banners displayed the words "forever a blue, forever a legend" and his name was sung by Chelsea supporters shortly after Fabregas' goal.
"Talking to the Chelsea players and their staff on the pitch, they were saying how good the way we were playing was".
His side spent long periods of the game without the ball but they competed against the FA Cup holders, who are yet to taste defeat this season. Mount also went close late on and the huge travelling support bounced with pride throughout the 90 minutes. "Doesn't everybody?" Lampard told Sky Sports.
If Derby do end up knocking out Chelsea, there would surely be different questions being asked of the club, as is the work of the fans and pundits, so it is best to leave their business alone.
DF Gary Cahill, 5 - His relative lack of comfort in possession and mobility are the main reasons why he has spent so much time on the bench this season, and Derby targeted the limitations in his game with their fast attack.
Marriott has been directly involved in six goals in his past five games for Derby in all competitions (four goals, two assists).