The Blues looked down and out 55 minutes into the game when Donny van de Beek fired Ajax 4-1 ahead at Stamford Bridge.
In a chaotic night in west London Chelsea had gifted their opponents two own goals through Tammy Abraham and Kepa Arrizabalaga, with Quincy Promes also scoring.
Jorginho was the only man on target for the hosts, converting from the penalty spot after four minutes on what appeared set to be a forgettable night for Lampard's men.
There was a further twist to come, however, as Cesar Azpilicueta pulled one back before Jorginho added his second penalty of the game, while in the same passage of play Ajax lost both central defenders to red cards.
Reece James then jumped off the bench to level at 4-4 and both teams subsequently had chances to take all three points, Azpilicueta seeing a goal chalked off by VAR for handball while Edson Alvarez and Noussair Mazraoui forced late saves from Kepa to maintain parity.
It was an incredible evening of football at Stamford Bridge, and even Lampard struggled to sum up what he had just seen.
"I can't explain the game. For all the things we might analyse back, the madness of the game, we are here for entertainment I suppose and anyone who watched that has to say what a game of football," the manager told BT Sport.
"Respect to Ajax, what a spectacle.
"I don't think I have been in a game like it. The two own goals were the story of the first half. I said at half time it will be 3-3 or 4-4, we were so in the game."
Lampard admitted that he was not pleased with the slack defending that allowed 2018-19's Champions League semi-finalists to net four times while calling into question the relatively mean allotment of stoppage time at the end.
"We looked dangerous and I felt we would build momentum. I am not happy overall, this is the Champions League and we made too many mistakes," he added.
"The biggest pleasure is the spirit the whole stadium showed. I can't give you much on the red cards, I didn't really see what they were for.
"At half time I would have taken a draw for sure. Let's take it as what it was. I was expecting somewhere towards 10 minutes of added time, not sure where four came from."