Chelsea's goal was scored in the eighth minute by Belgian striker Michy Batshuayi, a player the club bought for $62 million.
Lampard was appointed Chelsea boss on a three-year deal last Thursday after leading Derby to the Championship play-off final, where they lost to Aston Villa, in his first season as a manager.
Chelsea were held 1-1 by League of Ireland side Bohemians in Dublin, just days after Lampard was officially unveiled as Maurizio Sarri's successor.
"[Moving the ball fast] is his idea of how he wants to play the game".
Another career highlight for a player who featured at the Club World Cup during his two-year stint with Wellington, Molloy celebrated the memorable 89th minute strike with an equally impressive somersault - the same celebration he used to perform at David Farrington Park in Miramar.
"This game was very early but the other players are back other than the injured boys and Pulisic is not with us yet but you will see some of them at the weekend", Lampard added.
"I wanted to stretch them a bit and put them under pressure, it's what pre-season is about".
We could play over 60 games again this year, and from early July we're already being milked for every penny. But I refuse to get caught up in, 'Because a famous footballer is loved by a club, it's going to work.' It honestly makes little to no difference in the long term, it's whether you're a good manager, that's what it comes down to.
"We wanted to win the game, but it's not about that".
Pre-season preparations will continue in Ireland on Saturday when they take on St Patrick's Athletic. "It's about individuals getting fit and pushing themselves to the limit".
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