The 28-year-old scored for the third consecutive match in his side's impressive 3-0 Premier League win at Stoke City on Saturday.
Lennon, capped 21 times, last played for his country in their friendly win over Brazil in February 2013, but Martinez feels he remains a viable option for the tournament in France.
"Obviously it is not down to me but I get the opportunity to work with Aaron day in, day out, and he is such an important player," said the Goodison Park boss when asked about Lennon's international chances.
"We all know the quality he brings - the pace, the one v one ability, the work-rate, the understanding. That experience he has is invaluable.
"There are other players in that position, but I think he is showing he can be of incredible value to any squad and clearly for his national team he could be a real help."
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Martinez also had warm words for striker Romelu Lukaku, who overcame a back problem to ensure he kept his record of starting in every one of his team's league games this season at the Britannia Stadium before opening the scoring from the penalty spot.
"He has had injury problems but he doesn't want to miss games," added Martinez.
"He only managed to train on Friday slightly but the moment he felt he could walk freely he wanted to be available. It shows the incredible, strong personality he has.
"You run out of compliments you can pay to Rom. He lives for the game. He is an old-fashioned footballer, at the age of only 22.
"He just comes in and wants to work on his game constantly. He is a goalscorer who is obsessed with finishing quality."