The Chelsea boss paid tribute to the veteran midfielder following his two-goal haul against West Ham in the Blues' 3-0 win on Saturday evening
Lampard, who came into the fixture in his worst goalscoring draught in a decade, opened the scoring after the Brazilian Oscar had been fouled in the penalty area, following a mistake by full-back Guy Demel.
The England veteran would cap the victory late in the second half, and Mourinho dismissed claims that he needed to deliver a performance of this calibre.
"I think he's in a moment where he has nothing to prove, to you, to the fans, to me. He has nothing to prove," spoke the Chelsea boss.
"I was his manager in the best moment of his career, probably, and now I'm back for the final years. He must enjoy what he likes to do, which is enjoy football. Scoring is part of his DNA.
"He played very, very well," Mourinho continued. "Another who was very comfortable on the pitch. He benefited from the protection offered from [John Obi] Mikel. After that, Lamps felt a bit more freedom to find theses shooting areas."
Sandwiched between Lampard’s strikes was an impeccable finish from Oscar. Collecting the ball from Hazard, the former Internacional man spun, held off James Collins, before placing the ball past Jaaskelainen with ease, an example, according to Mourinho, that embodies the midfielder’s talent.
"I think the same as you think," Mourinho responded, when asked how well he felt Oscar performed. "In the middle, on the sides, he works hard – he covers – and when he has the ball he's able to score.
"It's not easy to succeed in this country, especially when so fragile, but his talent is amazing."
The Chelsea boss admitted that the second half miss from Maiga proved a crucial moment in the match, insisting that "2-0 is never enough" against sides like West Ham. That said, he felt his side were more than worthy winners.
"The game was good for us, and it became very comfortable," he continued. "We deserved this, we were very comfortable in the game, and everyone in the ground would see it."
Defeat for West Ham prolongs their burden of the worst home record in the league. Speaking after the match, manager Sam Allardyce agreed that Chelsea were deserved winners, albeit having capitalised on his side’s shortcomings.
"We allowed them to be good after the goal. But today is one Chelsea deserved to win," said Allardyce.
"Sadly it was our defence which broke first. When you make a mistake like that, gifted them a goal. It was always difficult from then on.
"We're suffering in front of goal, and now we're suffering defensively. We play with one front man, we don't play with one front man. We play with two front men, we don't play with two front men.
"It doesn't matter what system we play," he continued. "At the minute, we're missing chances."