The Belgian striker signed for the Red Devils from Everton back in July and has made a superb start to life at Old Trafford.
"Good age, 24, global player", said Keane on ITV. And Mourinho concedes the 24-year-old's workload will not get lighter until Ibrahimovic returns, which the United boss has suggested may not be until the new year.
With United sitting pretty at the top of the table after today's final whistle at Old Trafford, they have Lukaku's incredible scoring feats to thank once again for their excellent start to the season.
"We always expect a striker to score more goals than the others but especially our attacking players, they have the freedom to play", said Mourinho.
Lukaku has been named in the Belgium squad for qualifiers against Bosnia and Cyprus during the worldwide break, along with midfielder Marouane Fellaini, who is nursing an ankle injury.
Walcott & Wilshere miss out as Alexis, Lacazette & Iwobi all start
Arsene Wenger has now beaten 45 different opponents in the @ premierleague , more than any other manager (Alex Ferguson, 44). With the result all but settled, the game became a means for Sanchez get the goal his efforts deserved.
It was not just that they won 4-1 in Moscow; it was the way in which they did it - epitomised by the demeanour of CSKA manager Viktor Goncharenko, who confessed he felt "destroyed" by the movement and the pace of Anthony Martial, Henrikh Mkhitaryan and Romelu Lukaku. It's Roberto's responsibility. I can not, professionally speaking, say do this or do that, you know.
Lukaku scored 25 goals for the Toffees last season in the Premier League, narrowly missing out on the Golden Boot - who went to Harry Kane - by just four goals.
He said: I don't want to speak about his progress.
"That is exactly what we are looking to do and I think we've got the squad to do it". I think it was a bargain at £75m.
"Since his first loan to West Bromwich Albion, grabbed the opportunity with both hands, fighting for his evolution".
"And now of course I think Manchester United is a different level of expectation and he's coping well".