Cole’s former Blues team-mate is in his second season in charge in west London and currently has the team in the thick of the early Premier League title running as well as through to the last 16 of the Champions League with two group games to spare.
Lampard was initially hamstrung by a transfer embargo as well as the departure of key man Eden Hazard to Real Madrid after leaving Derby County to succeed Maurizio Sarri in July 2019 and later saw Chelsea fail to secure any deals in January, but worked around those setbacks by handing chances to several talented youngsters, eventually guiding the club to a fourth-place finish and the FA Cup Final.
A £200million summer spending spree subsequently piled big pressure on one of Chelsea’s most successful former players to strike a successful balance and build on that promising first season.
Trophies are now the obvious expectation moving forward for Lampard with the players at his disposal and Cole believes he is on track to achieve such success.
“I think he's been faultless,” Cole told BT Sport. "He took over, wasn't able to bring anyone in, and Chelsea lost their talisman Eden Hazard that summer, so he had to restructure the team.
"He brought six or seven players in through the academy, put down a style of play, an ethos, and they had a great season.
"Then all the signings he has brought in have made an impact, in the hunt for the league, qualified in the Champions League... I think he's been faultless, and it's great to see young English coaches get the chance and deliver - the same with (Rangers boss) Steven Gerrard. Two great icons of the game cutting their teeth in management and doing a great job.
"The expectation at Chelsea is to win trophies. Frank knows that.
"I think Frank will be treated the same as every manager - the same pressure he is under (is) you have to deliver at the club. But certainly I feel like they are well on course to winning trophies again and it is an exciting time for the club."