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Champions Juventus are 12 points behind Inter in third after beating Napoli 2-1, as Paulo Dybala scored on his return after nearly three months out and the league's leading scorer Cristiano Ronaldo also on target.
Both fixtures had been rescheduled because of coronavirus outbreaks at Inter last month and Napoli in early October.
Lukaku got his head to an Ashley Young cross to score his 21st league goal this campaign after in the 10th minute at the San Siro and then laid on Lautaro for the second midway through the second half.
Hamed Junior Traore pulled a goal back for the visitors with five minutes to go and Lukaku had a goal ruled offside before Inter claimed a 10th consecutive league win to strengthen their grip on the title.
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Antonio Conte's side are on course for a 19th Serie A title and first since 2010.
Juve's push for a 10th consecutive league title had faltered after taking just one point from their last two league games against lowly Benevento and Torino.
However their win against Napoli was crucial for their Champions League ambitions next season with both teams equal on points in fourth place before kick-off in Turin.
Juve were without Leonardo Bonucci and Federico Bernardeschi who tested positive for Covid-19 after international duty with Italy.
Dybala started on the bench, having being dropped for the derby match with Torino last weekend after breaking lockdown rules with teammates Weston McKennie and Arthur Melo.
Ronaldo missed a chance to put the champions ahead after two minutes when headed wide, before Napoli's Piotr Zielinski also fired over not long afterwards.
But good work from Federico Chiesa allowed the Portuguese to net 25th Serie A goal this campaign after quarter of an hour.
Chiesa beat two defenders before rolling the ball across to meet Ronaldo who finished off low past Alex Meret in the Napoli goal.
Veteran Juventus keeper Gianluigi Buffon did well to deny Napoli's Giovanni Di Lorenzo after the break and Fabian Ruiz midway through the second half.
Dybala came off the bench along with McKennie with 20 minutes to go and the Argentine had an immediate impact, curling in a Rodrigo Bentancur cross four minutes later.
Lorenzo Insigne pulled a goal back from the penalty spot in the final moments after Victor Osimhen was brought down by Giorgio Chiellini in the box.
Juventus overtook Atalanta to move third with the two teams meeting in Bergamo next week, when Inter travel to Napoli.
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