The current Belgium boss believes that the striker, who has hit the ground running under new manager Jose Mourinho, has fully matured into a superstar striker following his big-money move to Old Trafford.
The 24-year-old has scored seven goals in the Premier League so far – the top goalscorer – and has been part of a free-flowing and attack-minded Manchester United side who currently sit joint-top in the table.
Martinez believes that Lukaku – who he manages on international team duty – has done more than enough to quell critics of his blockbuster £75m transfer, as there was pressure for the striker to deliver straight away after it emerged that Zlatan Ibrahimovic was facing a lengthy time on the sidelines with an injury.
The former Toffees boss feels the striker has improved over such a short amount of time and will only improve under Mourinho.
“I have seen a difference in the maturity of Romelu since his move to Manchester United,” Martinez 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 ten-month competition.”
Manchester United are currently joint-top of the league alongside crosstown rivals Manchester City with 19 points – with just one goal the difference between the two sides.