Star striker Lukaku struck twice in the second half in Brussels to send Roberto Martinez's men top of their Nations League group with a hard-earned 2-1 victory.
The 25-year-old had gone scoreless in six competitive matches before Friday, last netting for United in a 2-1 win at Watford almost four weeks ago.
But ahead of Chelsea's clash with Lukaku and company in the Premier League next weekend, Hazard was not entirely pleased to see his international team-mate rediscover his scoring touch.
"It's not a good sign that Romelu scored tonight, because I'm playing against him with Chelsea very soon," Hazard told RTL.
"If he scores with Belgium it's fine, but it would be a good thing if he does not with Manchester United."
Belgium boss Roberto Martinez was perhaps more thankful for Lukaku's double, which came either side of Mario Gavranovic's 76th-minute equaliser.
The Red Devils are now three points clear of Switzerland at the halfway mark in Group A2.
UEFA Nations League (@UEFAEURO) October 12, 2018
"Romelu is a sensational goalscorer, his stats speak for themselves," Martinez said.
"What he has been doing on the international level in the last two years says enough. He is one of the best-performing goalscorers today.
"This win is very satisfying because it was a difficult match against Switzerland, who wanted to play.
"Of course we can play better football but must also be able to find solutions in this kind of game."