Her attack comes after the ALDE deputy last week visited Lithuania as part of a parliamentary delegation following up the 2007 parliament inquiry report on European collusion in extraordinary rendition and torture.
She was deputy chairman of the report and co-rapporteur of a new report aiming to determine European states’ progress in investigating and determining accountability in the last five years.
Six years after the first revelations about the abduction, torture and detention on European soil of terrorism suspects by the CIA, parliament is preparing a new report about the scandal.
Hearings were organised with NGO's and human rights institutions to gather additional data about some member states governments' alleged complicity in the rendition programme.
The report investigated claims arrangements existed in Lithuania, Romania, Poland, Denmark, Finland and Britain. Parliament sent a delegation to Lithuania last week before presenting the final report to the civil liberties committee in July.
The document will be voted on in the parliament's plenary session in September.
On her return, Ludford said, "Credit must go to Lithuania for having instituted both a parliamentary and a prosecutorial inquiry, more than any other country.
"This positive example shames bigger states, like the UK under the Labour government, which have refused to lift the lid."
She added, "However certain questions remain about Lithuania's role and MEPs encourage the prosecutor to examine new material.
"This relates notably to the claim to have been rendered and imprisoned there from current Guantanamo prisoner Abu Zubaydah, whose case will in any event have to be answered by the Lithuanian government before the Strasbourg court."
"Our visit to a building identified as a possible detention site confirmed that its construction and design fitted such a purpose. It is puzzling to conceive of what alternative use the prosecutor could have been persuaded it had."
"The prosecutor should fully extend his work, and of course the US which holds the truth must share it with its own and European citizens.
"Illegal rendition and torture demand full political and if necessary criminal responsibility, and Charles Taylor's conviction shows that impunity does not last," added Ludford.
Further comment came from Gerald Staberock, secretary general of the World Organisation Against Torture, who said, "Nothing has been done in member states to truly investigate and get to the bottom of the problem.
"There is an obligation not only not to torture or to be an accomplice in torture, but there is an obligation to investigate, to ensure accountability."
Many of the inquiries conducted in recent years by member states have been classified.
Those findings were not made available for the follow up report that parliament is preparing and the report’s author says a joined up approach is imperative.
MEP Hélène Flautre, rapporteur for civil liberties committee, commented, "Acknowledging the failures or difficulties members states have had in tackling the problem, the EU should take this issue into its own hands so that finally, the information can become freely accessible."
An inquiry established that CIA aircraft had landed in Lithuania on repeated occasions and that facilities were prepared for holding detainees.
However that and a subsequent prosecutors' inquiry found no proof of detainees having been there.