Lampard has made a positive start to life in management and heads to Old Trafford with his side full of confidence following their 3-1 win over high-flying Brentford at the weekend.
Saturday's 1-1 home draw against Wolverhampton Wanderers killed off the momentum that United had worked so hard to build up, which is becoming a familiar theme in Mourinho's two-and-a-half years in Manchester.
Already a Premier League title charge looks improbable, even if we are only six games into the campaign, as the Red Devils lag eight points behind early pacesetters Liverpool and have only faced one member of last term's top six so far.
It has been an indifferent start to the campaign at best for Mourinho, who had seen his side overcome Burnley, Watford and Young Boys in successive matches prior to the Wolves setback.
Back to square one, the Portuguese may now be tempted to field a stronger-than-expected lineup in midweek to at least keep United on course for silverware in the EFL Cup, a competition that has served him well down the years.
Mourinho has lifted the cup on four occasions, including in his maiden campaign at Old Trafford, but there is a sense that the Special One has since lost his magic touch. Despite the Red Devils' slow start to the season, though, they are still backed as second favourites to go all the way in the EFL Cup.
United do not have the best of recent records in English football's secondary competition, having won it once in the last eight seasons, with that triumph in 2016-17 one of just two major trophies won by Mourinho since taking over from Louis van Gaal - the other being that season's Europa League.
If United and Mourinho are to add to that tally, they must overcome a Derby side seemingly on the way up. The Red Devils tend to do well in such fixtures, as they have won their last five home meetings with Championship sides in normal time.
Amid further complaints regarding Mourinho's style of play, with Paul Pogba pulling no punches in his post-match debrief at the weekend, this third-round tie has now taken on added significance for English football's most successful club.
Recent form (all competitions): LLWWWD
Lampard was a two-time winner of this competition as a player, going all the way with Chelsea in 2005 and again two years later during Mourinho's first spell at Stamford Bridge.
The transition into management has not quite been seamless for the Chelsea legend, with back-to-back defeats at the hands of Leeds United and Millwall early in the season seeing some questions asked of the rookie boss.
Five wins in seven matches have followed in all competitions, though, and Derby are now into the third round of the EFL Cup and up to sixth in the Championship table, two points off leaders Leeds and Middlesbrough.
By the very nature of the second tier, the Rams could find themselves in the bottom half of the division with a single defeat or indeed at the summit. With games against Bolton Wanderers, Norwich City and Queens Park Rangers to come, Lampard will be targeting the latter scenario.
Before those quickfire league outings ahead of the international break, County have this bonus match at Old Trafford to look forward to - their second visit here in less than eight months.
The Rams saw off Oldham Athletic 2-0 in the first round and second-tier rivals Hull City 4-0 at the KCOM Stadium in the last round, cruising over the line with the help of highly-rated youngster Mason Mount.
The Chelsea youth product rounded off the scoring on Humberside and now has five goals and one assist in 11 outings this term, building on an impressive campaign in the Eredivisie last time out that saw him register a combined 23 goals and assists for Heerenveen.
Seven wins and a draw from his first 11 games in senior management is not bad going for Lampard. In this first managerial clash with Mourinho, the 40-year-old now has a chance to land a killer blow on his former mentor.
Recent form (all competitions): WWWLDW
Mourinho has already confirmed that he intends to hand Diogo Dalot just his second start for the Red Devils at right-back, a week on from his promising debut in the win at Young Boys.
Ashley Young has not featured on the opposite flank since the win at Watford, but may be restored here to give Luke Shaw a breather, while Sergio Romero is in line for his first appearance of the season in goal.
With Marcus Rashford sitting out the final match of his three-game ban, and Romelu Lukaku likely to be rested from the off, Mourinho may use out-of-form Alexis Sanchez and out-of-favour Anthony Martial in his attack.
Manchester United possible starting lineup:
Romero; Young, Lindelof, Smalling, Dalot; Pereira, Matic, McTominay; Sanchez, Martial, Mata
Derby County possible starting lineup:
Carson; Bogle, Keogh, Tomori, Malone; Johnson, Ledley, Mount; Jozefzoon, Marriott, Bennett
Head To Head
This will be the 107th meeting between the two clubs, with United winning 46 of the previous encounters, losing 31 and drawing the other 30.
The sides have not faced off in the Premier League since Derby's relegation a decade ago, but they have been paired together regularly in cup competitions since then.
In fact, they met at Old Trafford at the turn of the year when the Rams suffered a 2-0 loss here in the FA Cup third round - Jesse Lingard and Lukaku scoring late on.
We say: Manchester United 3-1 Derby County
This is a free hit of sorts for Derby, who have made a positive start to their Championship campaign and will head to Old Trafford in a buoyant mood. There is everything to lose for their opponents, on the other hand, with United - winless in two on home soil - in desperate need of victory to get their season back on track.