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.
Kemar Roofe restored Leeds' advantage midway through the half and the striker netted again after the interval before Ezgjan Alioski sealed the rout.
Leeds regained the lead through Roofe, the striker rising between two Derby defenders to loop a header beyond Carson from Alioski's left-wing cross after the home side had failed to clear their lines.
Jay Fulton scored the only goal as Swansea beat Preston North End to make it two wins from their opening two matches.
There was nothing the former England global could do about Roofe's second goal, though, the striker collecting a Klich pass and brilliantly spinning away from two defenders to thunder in a powerful drive that beat Carson at his near post.
"There were no surprises but we didn't deal with them".
"We were well beaten by the better team".
"There were a lot of lessons for us". The most disappointing thing for me is we went away from what we are.
Leeds are relentless under Bielsa though, rarely allowing opponents time to settle on the ball while they get forward quickly once they have possession.
He added: "I'm very much a left-sided player".
Derby looked to rally with new recruit Martyn Waghorn looking a threat but Leeds continued to prove menacing and two more flowing attacks led by Hernandez threatened to bring United a third with Joe Ledley and Richard Keogh also booked for hacking down the unplayable Saiz.
And just two minutes later United were in front thanks to a brilliant finish from Klich who received the ball on the edge of the area from Pablo Hernandez and then produced a gem of a shot into the bottom right corner for his second goal in two games.