Lampard told reporters he had to deliver a firm half-time team talk to rouse his players after they went in at the break trailing 1-0 to Pierre-Emerick Aubameyang's early headed goal.
"We were so awful for 30 minutes, slow lethargic, nervous. The second half was nothing to do with tactics it was all to do with spirit and desire. From my point of view you can accept a missed pass but you can't accept lethargy in a London derby. The players were told that and they delivered.
"I said my piece and it was pretty firm. You can't come here and have nothing about you. We are Chelsea, we can't just roll up. The lads started talking and it was a bit aggressive, which was a good thing. We made the change and it got better. We controlled everything in the second half, the fight and desire was here."
Arsenal were so dominant in the early exchanges that Lampard opted to make an early tactical change. He replaced Emerson with Jorginho on the half-hour mark and reverted to a back four:
The change helped Chelsea gain a foothold in the match, although they needed some good fortune to equalise on 83 minutes. Goalkeeper Bernd Leno misjudged Mason Mount's free-kick, allowing an unmarked Jorginho to tap into an empty net.
Jorginho had an eventful match after coming on as a substitute. Lampard said he was fortunate to escape picking up a second booking for a cynical foul on Lucas Torreira shortly before his equaliser:
Tammy Abraham netted the winner for Chelsea with just three minutes of normal time remaining to deny Mikel Arteta his first win as Arsenal manager and make it four straight home defeats for the Gunners.
The win also saw the Blues come from behind to win for the first time this season:
Nizaar Kinsella @NizaarKinsella
FT: Arsenal 1-2 Chelsea A first comeback of the Premier League season for Lampard's #CFC against rivals Arsenal. No new manager bounce for Mikel Arteta. It was cruel but glorious from the Blues. Arsenal will rightly complain that Leno mistakes and Jorginho didn't get sent off
Lampard's substitutions helped swing the game in Chelsea's favour, but Leno's error and the referee's decision not to send off Jorginho were also crucial to the Blues' victory.