The Belgium international has impressed for club and country over recent years, with his prolific strike rate earning him a £75 million move to Old Trafford this summer.
The 24-year-old is, however, yet to test himself on the grandest of stages, with 2017-18 set to see him turning out among Europe’s elite for the first time.
Ince is looking for Lukaku to embrace that challenge and show that he is deserving of a standing alongside the very best in the business.
The United legend told the Mail on Sunday ahead of an opening group stage clash with Basel on Tuesday: “It is highly unusual these days for a £75m striker not to have had previous experience and, if he wants to be considered world class, this is the stage where he has to prove himself.
“United's group opponents Basel, Benfica and CSKA Moscow will not be the acid test and he will not be fazed by them, but he needs to learn quickly so he is ready when the real elite stuff comes later in the season; knockout games against the likes of Barcelona, Real Madrid, Bayern Munich and Paris Saint-Germain.”
Lukaku was among the goals again on Saturday as he netted in United’s 2-2 draw with Stoke, but he has been warned that he will need to alter his game slightly in order to meet the demands of Champions League competition.
Ince added: “Lukaku is a goalscoring machine and would cause problems to any defence in the world because of the way he runs at people and keeps his composure in the penalty area.
“On the other hand, his retention of the ball is not fantastic and, if he goes chasing the ball to get involved in the build-up, United could get punished because top Champions League teams exploit opponents who have lost their shape.”
United head into their first continental clash of the campaign on the back of their first domestic setback, with a stalemate against Stoke bringing a run of three successive victories in the Premier League to an end.
While disappointed to have dropped points against the Potters, Ince believes Jose Mourinho’s side remain in good shape and sees them making positive progress at home and abroad.
He said: “People will accuse me of bias but I genuinely feel my former club United represent the Premier League's best chance of getting to the quarter-finals and beyond.
“Jose Mourinho knows how to win and will be going for the throat.
“United have great power in their line-up but it is not just power. Nemanja Matic and Paul Pogba might be 6ft 4ins but they can also play. Away from the spine, Marcus Rashford, Mkhitaryan, Jesse Lingard and Anthony Martial have the kind of flair that makes United well balanced.”