The new man in charge at Stamford Bridge saw his Premier League reign opened with a 4-0 defeat at Old Trafford.
United have failed to kick on from that point, with questions being asked of Ole Gunnar Solskjaer and an underperforming side.
Requiring penalties to see off Rochdale in the League Cup on Wednesday did the Norwegian’s cause few favours, with Chelsea showing how lower league opposition should be dispatched as they eased to a 7-1 win over Grimsby.
A heavyweight fourth-round encounter has now been put in place, with Lampard hoping to fare better in his next reunion with United than he did in his last.
The Chelsea boss said: “It's a big draw, two big teams and I'm pleased we're at home. We'll see.
“I think a lot can happen in football in a short time. The next round is not coming tomorrow. We have to respect the fact they have good players.
“They beat us 4-0... so I'm certainly not going to stand here and talk Man Utd down.
“It's going to be a tough game, and the beauty of what we did on Wednesday night was make the game look pretty easy.
“But these games can be tough and I'd rather, from a distance and having not watched the game, give Rochdale credit for taking them all the way. Man Utd will bring a strong team here.”
Chelsea are set to play host to United on October 29 and it could be that a number of youngsters figure once again for the Blues in that contest, with Lampard having handed out four debuts against Grimsby.
Teenage midfielder Billy Gilmour was also given a first start for the club, with the west London giants finishing a midweek cup clash with six academy graduates on the field.
Lampard, who has shown that he is willing to place considerable faith in youngsters this season, added: “I'm pleased some players who have not been playing so many minutes played, there were some debuts, and the young lads who came on improved the team, which was nice.”