The England international has impressed at Goodison Park since joining on loan from Tottenham in the last transfer window and made it consecutive goals in Premier League away games by scoring in the 1-1 draw at Swansea City on Saturday.
Manager Martinez has been impressed by Lennon's contribution, but told the former Leeds United player to keep up his high standards.
"The impressive thing about Aaron is he does not look like a loan player, he looks like he has been playing for Everton for many, many years and that is a very important sign," Martinez said.
"What we now want is for Aaron to carry on pushing, carry on enjoying his football, carry on keeping his place in the side and making sure he enjoys his time with Everton."
Martinez was also boosted by the return of Steven Pienaar after the midfielder missed the past four months with a knee injury.
The South African has made just nine league appearances in an injury-hit campaign and Martinez concedes that Pienaar has been a big miss.
"You see what we have been missing all season," he added. "Steven has been unavailable for 19 Premier League games and that is an astonishing amount of games to be without a key player."
