Hernandez made a great run to pull the ball back from the right for Alioski to head past Carson, and Saiz should have had a fifth for the visitors but miskicked with the goal at his mercy.
The damage, though, had already been as Leeds cruised to a victory that was even more impressive than the opening weekend win against deposed title favourites Stoke. 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.
Mateusz Klich bent home a stunning strike at the end of a thrilling team move to put the visitors in front inside five minutes at Pride Park on Saturday.
Lampard will now be charged to do better than that and take Derby back to the top flight for the first time since 2008, when the club was relegated with just 11 points.
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Leeds took advantage by breaking quickly and Samuel Saiz played the ball to Klich who fired a 25-yard shot past Scott Carson and into the bottom left corner. Lawrence smashed the free kick over the wall and through the grasp of Peacock-Farrell, who appeared to have the shot covered but could not stop it.
Promotion is a must for Leeds after hiring a head coach as decorated and established as Bielsa, and for now they certainly seem like prime candidates to go up. Carson was called into action to deny Roofe at point-blank range with Tomori making a last-ditch block to deny Ayling on the rebound.
The 24-year-old scored six goals in 42 games last term and with two in two already in this campaign, he will be one to watch throughout Lampard's debut season in management.
But it wouldn't be long before the third came, as Roofe received the ball in the penalty area and produced an exquisite turn to beat his man before hammering high into the net at Carson's near post.
Leeds struck again with devastating speed.