Since arriving from Derby County, Lampard has now won his first competitive game as a Chelsea manager.
And speaking after a 3-2 win over Norwich City, the 41-year-old trainer believes, in-form Mount deserves to see himself as a bona fide Chelsea player with his impressive performances.
"I spoke to Mason yesterday and asked him if he felt like he was a Chelsea player yet because it is important.
"He just sort of smiled. He's a confident boy, in a really nice way. He's got a humility and a work ethic, but he smiled and we had a laugh.
"I didn't really get a clear answer but he should feel like [a Chelsea player] if he plays like he is at the moment.
"And that doesn't mean it's the end of the story. He needs to work on getting better daily because he's a player who trains like it's a chance to improve and we need that feeling through the team.
"We want to win games, I want to stay in contention. I didn't want a slow start," the Blues boss said.
"We had a tough start and I have got to say I am happy with a lot of the performances, but you can't shout that too loudly if you aren't winning games.
"So it changes it for me, today. I am very happy. It gives me more determination to work."
The Blues will now focus on their next home game against Sheffield United on August 31.
