Lukaku scored in either half as Inter Milan claimed a 3-0 win against struggling Genoa on Saturday to move second in Serie A behind Juventus.
Antonio Conte’s side’s title ambitions took a knock with back-to-back stalemates against Roma and Fiorentina.
But they pulled back ahead of Atalanta, and within four points of leaders Juventus, who can however claim a ninth title in a row when they play Sampdoria on Sunday.
Lukaku nodded in the first after 34 minutes in the northwestern port city, with the former Manchester United forward completing a brace three minutes into injury time, to bring his tally to 23 league goals this season.
Alexis Sanchez, on-loan from United, was also on target with eight minutes to go, picking up a Victor Moses cross for his fourth league goal this season.
Atalanta were held 1-1 at AC Milan on Friday, with the Bergamo side due to meet Inter Milan in the final game of the season next week. Genoa are four points above the relegation zone with two games left this season.
Midtable Parma saw off relegated Brescia 2-1 in a win inspired by on-loan Juventus midfielder Dejan Kulusevski.
The 20-year-old Swede set up Matteo Darmian for the opener just before the hour mark before Daniele Dessena pulled the hosts level three minutes later. A spectacular solo effort from Kulusevski sealed back-to-back wins for Parma who had struggled after the lockdown.