Lampard was speaking ahead of their clash at Wolves.
Asked how he felt watching Mason Mount make his England debut, Lampard said: "Really proud. It's only [as a result of] the work he's been putting in since a young boy.
"We've all seen the pictures of him in a Chelsea kit – his dream has come true on two levels now. Now the hard work begins. This is where the scrutiny ramps up.
"He did well in both games. He needs to go up the gears and continue that progression because I think there's a lot more to come."