Blues defender Luiz was quoted by O Jogo newspaper as commenting on team-mate Lampard's widely-publicised problems with manager Andre Villas-Boas.
But the 24-year-old was adamant his words had been taken out of context and were not directed at Lampard individually but were more general in nature.
Claiming Luiz had criticised Lampard, O Jogo quoted him as saying: "No one has to be someone's father or son in a football club.
"There are no privileged people there. He simply has to listen to the coach when he gives orders and take them. No player can forget that they are just an employee of the club."
But Luiz tweeted on Thursday afternoon: "This is media, Frank know me, and I never said about him! I said generaly! I only talked about coaches and players in general. Always CFC."