Speaking ahead of Chelsea's 1-1 draw with Bohemians on Wednesday, Luiz expressed his enthusiasm about Lampard's appointment.
Striker Michy Batshuayi put Europa League winners Chelsea ahead in the eighth minute before trialist Eric Molloy levelled late on to snatch a draw at Dalymount Park in Dublin.
Despite the result, Lampard - in his first game as head coach of Chelsea - was satisfied with his side.
"We've only been back just a few days so there had been some pressure on the lads and we have been working them very hard".
"Fitness was always going to be an issue against a team that's halfway through their season". It's about individuals getting fit. Some of the performances, especially from the young lads today was really good.More news: JUST IN: Man detained in Buckingham Palace forecourt
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Lampard started with a 4-2-3-1 formation, with Cesar Azpilicueta at centre-back and Danny Drinkwater alongside Ethan Ampadu in midfield.
After the break, there was run-outs for a number of players who spent last season on loan away from the club, including defender Kurt Zouma and midfielders Tiemoue Bakayoko, Lewis Baker and Izzy Brown.
Given how much the average Chelsea supporter pays to go to the games or watch them on premium TV all year, the fact that what is effectively a preseason fitness session is being charged for is a bit of a farce.
"Lamps, or should I say "Gaffer", is now our leader and he's going to try to do everything he can like he did when he was a player, and now it's up to us to help him build the spirit and the philosophy around the club to be successful".
"You've lost your best player that half of everything was built around last season in Hazard, you can't actually buy anybody else at the moment and that [the Federation Internationale de Football Association ban] looks like it might stick".