The Belgium international has largely operated as a lone forward and Cole, who partnered Dwight Yorke, Ole Gunnar Solskjaer and Teddy Sheringham in United's treble-winning season in 1999, said the 24-year-old had exceeded his expectations.
"It's difficult to be a lone striker and especially if you don't get the service... it could be described as the graveyard shift because it is tough," Cole, who played nearly 200 league games for the club, told United's website (http://www.manutd.com).
"He has played the majority of games (this season) and that says a lot about him. He has not been injured and, for his first season, I think he has been top drawer."
Lukaku began the season strongly but went off the boil, going without a goal in seven games in all competitions between October and November. He has since found form and scored his 100th Premier League goal against Swansea City last weekend.
"Sometimes people have questioned Romelu and said he hasn't done this or that, but you have to be brutally honest: if you don't get the service as a lone man it is tough," Cole said.
"I think it has probably been a lot tougher than he would have thought and he appreciates that you can't have a weekend off at United, which he could have done at his previous clubs Everton and West Bromwich Albion."
Second-placed United have 68 points from 31 games and will look to deny leaders Manchester City the win they require to clinch the league title on Saturday.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by Toby Davis)
