In his first spell, Lukaku did not score in 15 appearances against Chelsea.
Although it was seven years in the making, and ten years since his last wearing the shirt, Chelsea proudly announced on their website that Romelu Lukaku had "come back home" earlier this month.
On Sunday, his second appearance against Arsenal was a success. Lukaku opened the scoring with an "unplayable", but "dominant" performance that the player described as "dominant".
This was his first goal for club after failing to score in his previous three years at Stamford Bridge and 15 previous appearances between 2011 and 2014. He was an obscure figure who was never given a Premier League start and was never able to score.
European champions Chelsea won 2-0 against their London rivals. There are early signs that Thomas Tuchel's side with Lukaku aboard will struggle to stop this season.
"What a beginning for Lukaku"
After moving to Everton and Manchester United, Lukaku, a Belgian international, returned to the club he had supported as a child for a second spell.
Lukaku, 28 years old, became the second-most expensive Premier League player after Manchester City's 100m Jack Grealish.
He did not disappoint against Arsenal, showing the same form that helped him rebuild his reputation in Italy.
Lukaku started in a perfect manner, tapping in after only 14 minutes. He celebrated by putting his finger on his lips and tapping in with his third touch of game. Bernd Leno made a great save, touching Lukaku’s diving header onto the bar.
He completed 19 of his 20 passes against Gunners, and contested 15 duels, more then any other player.
Arsenal 0-2 Chelsea: Lukaku looked dangerous - Tuchel praises Chelsea's new signing
"What a start Lukaku," boss Tuchel said to BBC Radio 5 Live. He struggled at first to touch the ball. He became very integrated after that.
He has already proven his worth to the squad. He was able to connect with Mason Mount and Kai Havertz at the front, and added something to our game that we didn't have.
Lukaku answered Sky Sports' questions about his performance. Every time I improve, I strive to be better. Although I still have a lot to learn, today was a good day.
"I worked hard all week. We knew it would be a huge game, and we won. As an individual, I want the team to succeed and I intend to keep doing so."
"His touch was impeccable"
Lukaku caused Arsenal defender Pablo Mari an especially difficult afternoon
Timo Werner only scored six goals in the top flight last season, despite scoring an expected goal rate (xG) of 11.5, while Lukaku scored 24 goals with an xG score of 23.8.
Chelsea, as a team, scored 58 goals in league, with a conversion rate 10.4%. This is lower than Inter Milan's 16.1%. They also won the title with 89 goals.
Lukaku's main strength was holding the ball up with his back towards goal. This gave Arsenal defender Pablo Mari a difficult time.
The Blues fans, who were seated in an area of Emirates Stadium, entertained Lukaku and continued singing his name until the end. Lukaku responded by waving, applauding and then putting his badge on.
Clinton Morrison, BBC Radio 5 Live pundit, said that "I think it's been a brilliant debut by Lukaku." He went away and improved his game. He understood what he needed to improve his game.
People used to be critical of him when he was at Manchester United because he didn't have a great touch. But today, his touch is flawless. He is a master of passing the ball and running with it. He will be a great signing.
"Last year, Werner wasn't holding the ball up. I believe that Lukaku will be able to help Werner, who isn't a natural number nine. Chelsea already have this and Lukaku is unplayable.
Chelsea finished fourth last year, 19 points behind winners Manchester City. However, they won the Champions League. They have started this season with two wins from their first two games, without conceding a goal.
Tuchel said, "We are still living in reality. Last season, we finished fourth and needed support from our competitors. We have shown that we are capable of producing top performances in the past half year.
"We feel that there is something we can improve on and we want to close that gap."
