Martinez worked with Lukaku during the pair's time together at Everton, where the 24-year-old impressed enough to earn a £75m summer switch to Old Trafford in July.
The former Chelsea and West Bromwich Albion ace has hit the ground running at his new club, scoring 11 goals in the opening two months of the season, and his national team manager believes that there is still more to come.
"I have seen a difference in the maturity of Romelu since his move to Manchester United," he told The Sun. "He is still a very young player but he has coped easily with the expectations and whatever Man United put on him.
"I can see he is really enjoying being in a team where there is very little margin for error. He is one of those players that sets himself little targets and you can see he's on track. For us, it's important that we see that continue over a 10-month competition."
Lukaku is currently nursing a minor ankle injury that has ruled him out of Belgium's meeting with Bosnia-Herzegovina on Saturday evening.