Lukaku scored a brace for the Blues in their 3-0 victory over Aston Villa.
The Belgian striker never scored at the Stamford Bridge Stadium in his first stint with the club.
And having accomplished his dream of putting his name on the scoresheet at Stamford Bridge after completing his return from Inter Milan, Lukaku couldn't hide his emotions after scoring.
"It's my dream since I was 11. I've worked hard for this moment," said Lukaku.
He added: "I was up and down at the start [of my career] but I've found a certain consistency in the last three years. With experience and hard work, I just keep on working.
"It's a good start but we have to keep working. We know this year's going to be very competitive. A lot of teams are going to be fighting for the title."
Chelsea are yet to taste a defeat in the Premier League as they currently sit second in the league table with 10 points, level on points and goal difference with table-toppers Manchester United.
Thomas Tuchel's Chelsea are the only second team in the Premier League to complete 600 wins and are behind Manchester United who have 690 wins.
Chelsea are keen on winning the Premier League title this season but will have to overcome stiff competition from defending champions Manchester City and in-form Manchester United who have re-signed their former goal-poacher Cristiano Ronaldo from Juventus.
Lukaku after helping Inter Milan to a first Serie A title in 12-years last term re-joined Chelsea for a fee in the region of £97.5 million on a five-year deal.
Since making his debut for the Blues against Arsenal, the bulky striker has buldged the net 3 times in three Premier League games.
