Lampard saw Leeds pull his team apart with pace and movement as his first home game in charge ended in a chastening defeat.
Leeds were full value for their 2-1 lead at the break but Derby went agonisingly close to equalising two minutes into the second half when a shot from Mount flew across the area with the sliding Waghorn narrowly failing to find a touch for what would been a tap in.
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.
The visitors held the lead for seven minutes as Derby levelled with a goal that will give Bailey Peacock-Farrell nightmares.
Four minutes later and it was four for the Whites, this time Alioski turning from provider to scorer as he powerfully headed home a Pablo Hernandez dinked ball in at the 64th minute, giving home keeper Scott Carson no chance.
The pace of Leeds was causing Derby problems and they were nearly in again in the 28th minute when Saiz powered through the middle, but his 20-yard shot was straight at Carson.
The West Yorkshire outfit were the better side from start to finish, and there was no doubt that the Rams did not deserve anything from the match.
Leeds got back in front through Kemar Roofer, scoring a looping header not all that dissimilar to Lawrence's winning goal for Derby last weekend. Carson made a great save and Tomori blocked the rebound.
The Rams lost 4-1 to Leeds United to come back down to earth with a bump following the opening day win at Reading eight days earlier, Lampard's men struggling to get a foothold on the game throughout.
"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".