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Pekarskytė's application is based on a provision in the citizenship law that took effect in July and envisages a possibility for people who can claim special merits to Lithuania to hold dual citizenship.
The Lithuanian laws bans dual citizenship as a matter of course, save for some exceptions.
"The application has been received and will now be processed by the Citizenship Commission," presidential adviser Liudas Zakarevičius told BNS.
The next meeting of the commission is planned in September. The commission will submit a recommendation to the president, while the final decision will be made by Grybauskaitė.
Pekarskytė, 35, was granted the Icelandic citizenship in 2012 and automatically lost her Lithuanian passport. The athlete represents the women's handball team of Iceland.