He spoke in Lagos on Monday during the Wole Soyinka Investigate Reporting award.
Falana said this while reacting to the denial of the DSS that its operatives never invaded the courtroom of Justice Ijeoma Ojukwu at the Federal High Court in Abuja on Friday.
Falana said he knew the names of at least five of the operatives that were in court, stating that he would make the names public when the time was right.
He urged journalists to desist from legitimising the lies of the government.
He said, “I will like to urge all of us, particularly the journalists not to peddle rumours.
“For a government to lie, it is a serious matter and we must take it up.”
Falana also condemned the two spokespersons for President Muhammadu Buhari, Garba Shehu and Femi Adesina, for peddling falsehood about the rearrest of Sowore.
He said that the statements released by the two advisers was an attempt to insult the sensibility of Nigerians, adding that both Shehu and Adesina must apologise to the Nigerian people for lying.