The former England international took over the reins of the west London side from Maurizio Sarri earlier this month following intense speculation.
Lampard was in charge of Derby Country for one season before he managed to land one of the biggest jobs in the Premier League.
The Chelsea FC record goal-scorer led Derby to the Championship play-off final last season but the Rams lost 2-1 to Aston Villa at Wembley.
Sarri impressed during his 12-month stint at Chelsea FC after the controversial Italian coach led the Blues to a third-placed finish as well as glory in the Europa League.
Speaking about his former team-mate and new manager Lampard, Luiz warned the Blues legend that his squad will need to deliver.
“If you keep winning titles, this is good. In the last years, we’ve changed coach but still won things,” Luiz told Chelsea FC’s website.
“Now, we have a different coach with a new philosophy. But in the end it is the same thing: you play for a big club and a big club has to win.
“Everyone knows Lamps is a legend. It was a pleasure to work with him as a player and it’s a pleasure to work with him as a coach now.
“When you play with a player like Lamps, he is a leader anyway so he is still leading the team now in a different place.
“He cannot run anymore and cannot score goals any more but he’s still a leader.
“The squad is good enough, with the experienced players, the talented players, the young players.
“We just lost a big, big name, a legend of the club, in Eden Hazard but we have many players who can do the job.”
Chelsea FC have added Borussia Dortmund playmaker Christian Pulisic and Real Madrid midfielder Mateo Kovacic to their squad in the summer transfer window.
However, the Blues are currently serving a transfer ban for the next two windows to limit Lampard’s ability to make drastic improvements to the squad.
Chelsea FC have struggled to find a level of consistency in recent years under Lampard’s predecessors Jose Mourinho, Antonio Conte and Sarri.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news