Derby won 2-1 against Reading away from home in the Championship last weekend, and on Saturday evening, the Rams were demolished 4-1 by Leeds at home.
Lampard's first game in charge of Derby had been less impressive as they scraped a last-gasp victor at Reading.
After last week's excellent outing against Stoke City, there wasn't really much expectation that today's game against Lampard's Derby County would be much of the same, yet it was.
Leeds should have made the points safe in the 56th minute but Scott Carson made a magnificent reaction save to keep out another Roofe header.
Derby had a bright start to the second half with Mason Mount dragging a shot wide but Klich set up Roofe to beat Carson with a rising drive on the hour before Alioski headed in Pablo Hernandez's cross four minutes later.
No other team has defeated United more times than Derby since 2010, getting the better of their opponents 10 times.
"I'm quick and like to get forward - when I was at Fulham I scored six goals and had a few more assists too".
Leeds need not have anxious about the near miss as they made it 3-1 on the hour, Roofe producing a great turn in the area to get clear before rifling a left foot shot into the top corner of the net.
"That's not to say we're not good enough, we certainly are but we need to be braver and can't play longer balls when we should be trying to get out because that's an easy option".
Lampard will be hoping to make it 11 wins over their rivals, as The Rams look to start their Championship campaign with back-to-back victories for the first time since 2011.
Lampard had raided his former club Chelsea for the services of the promising young defender Fikayo Tomori on loan for the season while Martyn Waghorn, who arrived from Ipswich this week, was given the chance to show what he could bring to the attack.