Mustafa al-Hawsawi, 50, has petitioned the European court that last year found Lithuania complicit in a secret CIA programme and ordered the EU member to compensate another terror suspect.
"Last week, the government received the Hawsawi petition through the European Court of Human Rights," Deputy Justice Minister Irma Gudziunaite told AFP.
She said Lithuania, a staunch US ally that joined both the EU and NATO in 2004, had until March 22 to submit its position.
The Strasbourg-based court ruled last year that Lithuania had hosted a secret prison in 2005-2006.
The court ordered Vilnius to pay 100,000 euros ($113,000) in damages to Abu Zubaydah, another Guantanamo detainee suspected of being a top Palestinian operative for Al-Qaeda.
Lithuanian officials, who deny the existence of any secret CIA jails on their territory, told the court that a building on the outskirts of Vilnius suspected of being such a site was "an intelligence support centre".
A pre-trial investigation into the allegations has been ongoing in Lithuania since 2015.
The Baltic state says the United States has refused to answer questions from Lithuanian prosecutors or provide requested information.
The ECHR ruled that fellow EU and NATO member states Poland and Romania also allowed the unlawful imprisonment of terror suspects more than a decade ago.