Chelsea appointed their record goalscorer as Maurizio Sarri’s successor earlier this month.
Lampard has penned a three-year contract with the Blues, who paid Championship side Derby County £4million in compensation to part company with the 40-year-old.
The Chelsea legend faces a difficult task to turn the west Londoners into title contenders as the club are currently serving a two-window transfer ban.
Lampard is expected to be given a minimum of two years to turn around the club’s fortunes, but Luiz believes fans could turn the heat up on him in six month’s time should the team not be in contention to win silverware.
“I think everyone understands the moment and everyone understands to be patient but in the end everyone wants to win,” Luiz told football.london.
“They are going to be patient in the first six months and then in the last six months they want us to win. It is going to be like that, we have to think about that and do the best to make them happy.
“If you don’t think like that [to win trophies] then you can’t play for Chelsea. The ambition has to be high. Of course, you have many, many fantastic clubs.
“They are working with the managers more than three or four years and they have amazing squads. Inside the pitch it is up to us to have to show our jobs.
“Even if you have a transfer ban I don’t know if the team needs more players or not.
“I think we are just talking about the transfer ban, but last season not at one moment were we talking about different names.
“I think the squad is good enough, with the experienced players, the talented players, the young players and I think 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.”
Lampard’s first competitive game in charge of Chelsea takes place on August 11 and will see last season’s Europa League winners take on Manchester United at Old Trafford.