Following a goalless first half, Leandro Damiao struck late in the second to earn the hosts a surprise win.
The Blues had looked the more dangerous throughout the match, but a late flurry from Kawasaki culminated in Damiao heading the winner in the 88th minute.
Chelsea's preparations for the 2019-20 season continue on Tuesday with a clash against Spanish champions Barcelona.
It was a frustrating 90 minutes for Lampard and his side, who found little rhythm despite dominating possession.
There were positives, though, as Christian Pulisic made his debut in a 25-minute cameo, and 20-year-old Mason Mount put in a good performance.
Michy Batshuayi provided the best opening of the first half when his first-time shot had goalkeeper Jung Sung-Ryong wrong-footed, but the effort whistled wide of the target.
Pedro's long-range strike sailed over the bar, and then Batshuayi set up Mount for an effort shortly before the break that was deflected wide.
Lampard wrung the changes at half-time:
Mount fashioned a good opening again soon after the break having linked up well with Ross Barkley, but his curling effort from the left went just wide.
After another attempt on goal, the playmaker was replaced by Pulisic in the 65th minute:
The American showed some fine touches and made some enterprising runs in his short spell on the pitch, but he could not fashion any chances.
Kenedy, meanwhile, worked Sung-Ryong on two occasions in the second half before Olivier Giroud had Chelsea's best effort from a free-kick, stinging the South Korean's gloves 15 minutes from time.
A goalless draw looked to be beckoning as the clock ticked into the last 10 minutes, but Frontale stepped up a gear.
Damiao headed onto the bar before Willy Caballero was forced into a fine save, but Kengo Nakamura stood up a fine cross from the resulting corner that Damiao headed home for the winner.