Lukaku made his ninth club goal of the season with 16 minutes to play and gave Everton their third win in four matches.
According to Sports24, Roberto Martinez made five changes to his starting line-up from the surprise loss against Sunderland on Boxing Day, with England left-back Leighton Baines returning after a broken toe.
As Captain Phil Jagielka was missing due to a hamstring injury, defender Antolin Alcaraz came in for his Toffees debut.
Goalkeeper Tim Howard and midfielder Gareth Barry were also absent due to suspension, so Joel Robles made his first Everton Premier League start in between the posts.
Everton looked no weaker than usual in the early stages as Coleman's third goal in four games fired them into the lead in the ninth minute.
The report said that Southampton drew level in the 71st minute as Ramirez collected the ball from Lallana and sent a dipping effort goalwards that seemed to elude Spanish goalkeeper Robles too easily on its way into the net.
Having received the ball from substitute Steven Pienaar as the Toffees swept forward, James McCarthy neatly set up Lukaku, who smashed home past Davis from 12 yards.
--ANI (Posted on 30-12-2013)