The 19-year-old caught the eye of Lampard during pre-season and was rewarded with a three-year contract in August.
Mills, the son of Lampard's former England team-mate Danny, has scored seven goals in eight games for the Toffees' under-21s this season.
In addition, he made his first-team debut off the bench in the 1-0 victory over Fleetwood Town in the Carabao Cup in August - and again could be in the squad for tonight's third-round tie at AFC Bournemouth.
There has been clamour from some sections of supporters for Mills to play a more prominent role in Everton's Premier League campaign - but Lampard believes patience is required with the versatile youngster.
The Goodison Park manager said: “The biggest thing will always be the individual, how good they are and what level of player, what level of attitude they have.
“Stan’s has a great approach and attitude. That probably comes from his footballing background and his dad, who I know well. He was a great athlete as well as a good player.
“Stan’s a very strong runner and has an eye for goal - he’s a good player. So, yes, he can be an option. But he’s still very young.
“We all know how hard it is at a young age to break through and have an immediate impact regularly, so it will be phased in for him but, for sure, he is progressing in the right way.”