Pierre-Emerick Aubameyang put Arsenal in front in the 13th minute with a fine header, a lead which they deservedly maintained for the vast majority of the game.
The Gunners were relatively comfortable until Bernd Leno flapped at a Mason Mount free-kick in the 83rd minute to allow Jorginho – who came on and changed the game – to sidefoot into an empty net.
Tammy Abraham then nicked all three points for Chelsea four minutes later after a wonderful touch and finish after Willian broke away and crossed for the English frontman.
Lampard told BBC Sport: “We were so awful for 30 mins, slow lethargic, nervous. The opposite of against Tottenham. We gave Arsenal everything they wanted. We made the change early, felt it had to be done. Second half we dominated.
“After 10 mins or so it was clear that Arsenal had seen us play against Tottenham and made us into a back five instead of a back three. They were on top and there was a lack of balance to our team. The sub gave us another man in midfield and gave us more urgency.
“From my point of view you can accept a miss-pass but you can’t accept lethargy in a London derby. The players were told that and they delivered. The second half was nothing to do with tactics it was all to do with spirit and desire.
“I still haven’t bounced back from Boxing Day mentally (loss to Southampton). Our next home games we’ll do everything we can to turn the corner. We’re still in fourth and want more and the home games have been different so we have to focus on them when they come around.”