The Spaniard managed Lukaku for three years earlier in his Everton career and went onto to become his boss at international level after his surprise appointment by Belgium.
The 24-year-old made the move to Old Trafford this summer in a £75m move and he has certainly hit the ground running with his new side, scoring seven goals in seven games in all competitions.
Lukaku continued his fine form during the recent international break, scoring four goals in two games to book Belgium's place at next summer's World Cup.
Speaking to 'talkSPORT', Martinez says that he was never in any doubt that Lukaku would get off to a flying start in Manchester, pointing to the player's incredible mind as a reason behind his success.
'It never crossed my mind that it would be something difficult for Rom. Everyone that plays with him or works with him realises very quickly that he has an elite brain,' Martinez explained.
'As a footballer, you can have your attributes but the focus he can have is quite unique. When he went to Manchester United he was solely focused on starting well and making a big impact and that is what he has done.
'He is still a very young player - sometimes we forget he is only 24 - but his goalscoring record is sensational and he is a player that wants to carry on developing and carry on learning. Now he is with a manager with whom he will keep learning different aspects at club level.'
The former Wigan boss went on to say that he has noticed a difference in Lukaku since his big-money move.
'I have seen a big difference in terms of his maturity when he comes to international camps,' pointed out Martinez.
'From the young player I signed from West Brom and Chelsea at that time, it is the same goalscorer but with an incredible maturity. That is great to see and he still has many, many years to develop.'