Signed from Everton at an initial cost of £75m (€85m), the 24-year-old hit the ground running at Old Trafford with 11 goals in his first 10 matches for the club.
The striker has since failed to score in his last five matches, with apparent fan agitation in Saturday’s 1-0 win against Tottenham getting under Mourinho’s skin.
The United boss said it was unfair that fans “don’t support him so much” as, whether he scores or not, the Belgium international makes a difference — frustrations he repeated ahead of tonight’s Champions League clash with Benfica.
“The fans are the fans, and they pay their ticket and are free to express themselves however they want,” Mourinho said.
“But my job is, when I feel they deserve, to protect my players and I feel Romelu is one of the players that should be untouchable in terms of the respect from everyone.
“It’s not one ball that hit the post or one save by the opposite goalkeeper that can make Romelu’s contribution below the top level.
“He’s playing extremely well for us and yes, I have to protect my players when I think my players deserve it.
“Romelu always deserves it because of what he does for the team, what he does for the team is fantastic.
“Playing football for a striker is not just about scoring goals.
“So for me he is untouchable for my team and untouchable also in the support and the respect that he deserves from the fans.”
Put to Mourinho that perhaps it is typical of a striker like Lukaku to have quiet moments, he said: “I don’t think he’s quiet at all.
“Ask (Toby) Alderweireld and (Jan) Vertonghen and (Eric) Dier if he was quiet! And they are some of the
best central defenders in football.”
Such sentiments were echoed by Lukaku’s team-mate Eric Bailly, who is pleased to be playing alongside the striker having faced him when Lukaku was at Everton.
“I think, like many people, that Romelu is a great forward,” the United defender said.
“I’ve played against him and now have the fortune to be playing with him.
“He is very important for us. Everybody can see everything is going well for him and I hope he can continue this scoring run and helping the team as he has been doing.”
Bailly returned from injury on Saturday and could feature against Benfica.
United will wrap up a place in the Champions League last 16 if they gain a better result than third-placed CSKA Moscow do against Basel.
Benfica have lost all three Group A matches to date but Mourinho is expecting a tough evening, having edged past them 1-0 in Portugal a fortnight ago.
“Our aim tomorrow is basically to qualify,” he said.
“Ten points would be OK for qualifying but our main aim is to finish first in the group.
“We know the statistics are what they are but Basel has had good results against CSKA and Benfica. A draw is not bad but Benfica will give us a difficult match.
“They have their own ambition and pride, and they will try to win but we want to get to the last 16 as first in the group.”
For his part, Benfica boss Rui Vitoria has backed young goalkeeper Mile Svilar to respond positively to his “trial by fire” at the hands of United.
A fortnight ago in Lisbon, 18-year-old Svilar carried Marcus Rashford’s free-kick over the line to hand United all three points from their Champions League trip to the Portuguese capital.
But ahead of tonight’s reverse meeting at Old Trafford, Eagles head coach Vitoria is convinced his teenage stopper is ready to put his debut mistake behind him.
He said: “Svilar had a trial by fire — it was his first game in the Champions League. He’s only 18, a very young age.
“But we only talk about him being 18 because his identification card says that. He actually shows maturity above his actual age.
“We are calm. Mistakes can happen to any player, whether young or older, but when we have maturity and quality we can face any situation and go into games with great conviction.
“He knows that to have a rosy future he will have to pass through these kinds of doors. He will play his part and he will be ready.”
Luisao will miss out after being sent off against United at the Estadio da Luz but home fans may well get to see his fellow defender Ruben Dias — a reported target for Mourinho — in action.
“He is a young player who is showing immense progression and significant development,” said Vitoria of the 20-year-old, who only made his first senior appearance for Benfica in September.
“He has huge potential and will improve a lot. We want him to stay with us for many years — he’s from our academy.
“As for any issues around his future elsewhere I cannot say anything else, that’s not my place.”