The Belgium striker set up two goals and also scored as Napoli won 4-0 at Cagliari on Sunday for their third straight victory in the Italian league.
Defending champions Inter Milan narrowly avoided a first defeat of the season as they salvaged a 1-1 draw at Monza.
There are positive signs that, under new coach Antonio Conte, Napoli are starting to look more like the team that stormed to the league title in 2023 and less like the troubled side of last season.
One of the stars of that team was the now departed Victor Osimhen and he was replaced by Lukaku - reuniting him with Conte after the pair won Serie A at Inter in 2021.
"I strongly wanted Romelu, as I always have throughout my career, because we're talking about an atypical player," Conte said. "He's not yet at his top level but he's a player who will become fundamental for us."
Conte lost his first league match in charge but Napoli have won all three since then, scoring nine goals and conceding just one.
Lukaku scored on his debut last time out and was given his first start for Napoli on Sunday.
He proved dangerous from the start and set up the opener in the 18th minute, rolling Matteo Politano's cutback across the area to Giovanni Di Lorenzo, whose effort was deflected by Cagliari defender Yerry Mina.
The match had to be suspended for around eight minutes in the first half because of crowd trouble.
Napoli had Alex Meret to thank for keeping them in the lead as the goalkeeper pulled off a number of great saves.
They doubled their lead in the 66th minute when Khvicha Kvaratskhelia ran onto a pinpoint throughball from Lukaku and fired into the bottom left corner.
Kvaratskhelia returned the favour four minutes later following a howler from Cagliari goalkeeper Simone Scuffet who, while trying to play out from the back, passed the ball straight to the Georgian. Kvaratskhelia passed to Lukaku for a simple finish.
Alessandro Buongiorno netted in stoppage time.
Ahead of Wednesday's Champions League match at Manchester City, Inter coach Simone Inzaghi rotated his squad and almost paid the price.
The Nerazzurri had a few early chances but looked relatively toothless.
Instead it was Monza - who had picked up just two points from their previous three matches - who took a surprise lead nine minutes from time when Dany Mota headed Armando Izzo's cross into the top left corner.
However, seven minutes later Carlos Augusto's cross was deflected into the path of Denzel Dumfries for a simple tap-in equaliser at the back post.
Ademola Lookman inspired Atalanta to a 3-2 comeback win over Fiorentina in their first home game of the season.
It was a first Serie A appearance of the season for Lookman, who scored a hat-trick in last season's Europa League final win.
Lookman set up Mateo Retegui for Atalanta's equaliser, either side of Fiorentina goals from Lucas Martinez Quarta and Moise Kean.
Kean also hit the post before Charles De Ketelaere leveled just before halftime. And less than 60 seconds later, Lookman scored what was to prove the winner with a delightful solo effort.
Roma were denied a first win of the season by Koni De Winter's stoppage-time equaliser, which salvaged a 1-1 draw for Genoa. Torino and Lecce drew 0-0.
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