Lukaku has made a blistering start to life at Old Trafford following his summer move from Everton, scoring 11 goals in 10 games for the Red Devils including seven in seven Premier League outings.
However, Saturday's trip to Liverpool marks the first time United will have played a fellow member of the 'big six', and Neville believes that Lukaku still has more to prove in the biggest matches.
"Romelu Lukaku has settled in brilliantly and done everything he was asked to do in terms of converting those home draws into wins, but games like this one are the real test," he told Sky Sports News.
"When I look back to the Everton striker's recent performances at Anfield he didn't play well, so this is the next step up for him. Going away to Anfield is a big test and his service will be more limited so he's now got to show the ruthless streak to win the big games for United.
"He will be defined by his performances in big matches. You're at a club with aspirations of winning things and a world class striker will be defined by trophies and performances in big matches."
Lukaku has scored five goals in 11 previous appearances against Liverpool during his time with Chelsea, West Bromwich Albion and Everton.