The striker, who sealed a permanent move to Goodison Park in July for €35 million, is not yet back to full fitness after representing Belgium at Brazil 2014
The Belgium international joined Everton from Chelsea in a club-record €35 million deal in July after a successful loan spell on Merseyside last season.
However, Martinez is wary of risking the 21-year-old against Leicester City next Saturday following his World Cup exertions in Brazil.
"When you have players coming back from the World Cup you have to decide if you want the players straight away or do you give them a bit of time to refresh and be ready to play for 10 months?" the Everton boss told reporters.
"It will only be Kevin Mirallas and Rom who might not start the season. For Romelu, it will depend on how he adapts to work from now until August 16.
"There is a degree of risk if you put them into a situation so early. They've been training really well and are accumulating a lot of work."
Martinez is willing to dip into the transfer market again following the arrivals of Lukaku, Muhamed Besic and Gareth Barry, but stressed that Everton's remaining business will depend on the fitness of Arouna Kone and Bryan Oviedo - both of whom are recovering from long-term injuries.
"Towards the end of last season I said we needed six more players, but it wasn't six new players, it was six players," Martinez added.
"We have added Barry, Lukaku and Besic and we also have Tony Hibbert who re-signed.
"We still need one or two, depending on how quickly Arouna Kone and Bryan Oviedo recover from their injuries."