The Blues moved top of the pile on Saturday when they came from behind to defeat Leeds United 3-1 at Stamford Bridge as fans returned to the stadium for the first time in 2020/21.
Patrick Bamford gave Leeds a fourth-minute lead, but Olivier Giroud followed up his four-goal Champions League haul against Sevilla with an equaliser.
Second-half goals from Kurt Zouma and substitute Christian Pulisic then completed the comeback.
Lampard is happy for fans to be ambitious after Chelsea moved into first place, but told his players to remain calm because they still have key improvements to make.
"There is certainly nothing wrong with the fans thinking that," he said when asked about growing hopes Chelsea can win the league.
"Great to have them back [in the stadium], their input was huge, the noise huge.
"You can see how excited they are at the end that we are top of the league.
"My job and our job is to know that it’s a long season and the next question is how consistent can we be with this form, how much we can improve, because I believe there is a lot more we can do and there will be a lot of challenges ahead.
"Enjoy it. I will have that small glass of wine, maybe a large one, but at the same time we need to make sure we stay grounded.
"But there were a lot of good things - to play against Leeds in the form they are in and the type of team they are and dominate in terms of chances was a real great performance from us."
One of the few negatives for Chelsea was a first-half hamstring injury for Hakim Ziyech, who was replaced by Pulisic.
Lampard added: "With Hakim it is a hamstring injury which we will find out the severity of in the next couple of days. It is obviously a disappointment going into this busy period.
"I was really pleased for Christian because it has been a difficult period with the injury for him, when he gets frustrated in a good way because he wants to play.
"To play in the period of the game he played, with the intensity of the game and get his goal - he has an incredible gift, it sounds simple, but arriving in the six-yard box as a wide man, that is where the goals are.
"So I was delighted that he got his goal and he is only going to get stronger now."