The Belgium international moved to Manchester United in a £75m deal from Premier League rivals Everton in the summer.
Lukaku’s move was met with some skepticism given his struggles at Chelsea before he moved to Everton in 2013.
The Manchester United signing scored 10 goals in nine appearances in all competitions to make a brilliant start to his season.
The 20-time English champions struggled in October and November following a return of two goals in 12 games.
The Red Devils striker scored two goals in successive Premier League games thanks to victories over Bournemouth and West Brom.
Lukaku didn’t celebrate his last two goals following his disappointing derby performance in Manchester United’s 2-1 loss to Manchester City.
Former Manchester City defender Mills attempted to explain Lukaku’s non-celebration.
“It’s an incredible goal haul. He is still getting a lot of criticism. Maybe it is starting to affect him,” Mills told BBC Radio 5 Live.
“He could be thinking he isn’t going to celebrate and just do his job.”
Lukaku scored 25 goals in 36 games in the Premier League last term in his final season at Everton.
Manchester United will take on La Liga side Sevilla in the Champions League round of last 16.
Lukaku wasn’t part of the Chelsea squad that won Europe’s top competition in 2012.
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