The Red Devils signed the Belgium international in a £75m deal from Premier League rivals Everton in the summer transfer window despite interest from his former club Chelsea.
Lukaku faced questions about his big-game temperament and ability to shine in a top Premier League team but the 24-year-old has answered his critics in emphatic fashion.
The Belgian forward scored what ultimately proved a consolation goal in a 2-1 loss to Real Madrid in the Uefa Super Cup in Macedonia back in August.
Lukaku has netted six times in six games in the Premier League to hit the ground running in the title race.
The ex Anderlecht forward netted twice in a 4-1 win at CSKA Moscow in the Champions League on Wednesday night to take his tally to three goals in the European competition this term.
Former Manchester City defender Mills believes Lukaku has already made improvements to his game since his big-money move to Manchester United this summer.
“Look at Lukaku. He has gone to a better club,” Mills told BBC Radio 5 Live.
“He is playing with better players. He is scoring more goals. He looks a better player already.”
Lukaku scored 25 times in 36 games in the Premier League last season for Everton to finish behind Tottenham striker Harry Kane in the goal-scoring charts.
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