Seventy-eight members of the Seimas backed a constitutional amendment allowing an impeached person to stand in elections, 16 votes short of the necessary 94 for the vote to pass.
Fifteen lawmakers voted against the amendment and four abstained.
A constitutional amendment must be voted on twice by the Seimas, with an interval of at least three months between the votes, and requires a two-thirds majority, or 94 votes, to be adopted.
The Seimas several years ago tried to pass constitutional amendments that would have opened the way for Paksas to run in elections, but failed to muster enough votes.
The latest amendment, submitted by the ruling bloc, would have allowed an impeached person to be elected president or a member of the Seimas ten years after his or her removal from office.
The amendment was tabled to comply with the Strasbourg-based court's 2011 ruling that the lifetime ban on Paksas to stand as a candidate in elections was disproportionate and ran counter to the European Convention on Human Rights.
Lithuania faces sanctions from the Council of Europe's Committee of Ministers, which monitors the execution of the Strasbourg court's judgments. The committee has already placed the country under the so-called "enhanced supervision procedure".
Paksas was ousted by impeachment in April 2004 after the Lithuanian Constitutional Court ruled that he had grossly violated the Constitution and his oath of office by granting Lithuanian citizenship to Yuri Borisov, the main financial supporter of his presidential election campaign.
The Constitutional Court has ruled that a person removed from office through impeachment can never again hold a public office that requires an oath and that the Constitution needs to be amended to lift the ban.