The escape plans were discovered in her diary.
Dennehy, 33, was then placed in solitary confinement for two years.
She claimed her human rights had been violated as a result and took her case for damages to the high court.
But judges ruled it was "necessary and proportionate" to place her in solitary confinement after hearing about the detailed escape plot.
Dennehy was given a whole-life sentence at the Old Bailey for murdering three men and stabbing two more.
She claimed that she had been left "tearful and upset" after being placed in segregation at HMP Bronzefield near Ashford, Surrey, since prison guards allegedly found a breakout plot in her diary.
Government lawyers have conceded the segregation period between September 21 2013 and September 4 2015 was technically unlawful because it was not properly authorised by former Justice Secretary Chris Grayling.
But Mr Justice Singh, sitting in London, ruled that her segregation since then had been "in accordance with law" and "at all material times it has been necessary and proportionate".
Justice Department barrister Tom Weisselberg QC told the High Court that a credible escape plot was found in her cell.
"Dennehy was segregated because a credible escape plan involving her and two other prisoners had been uncovered," he said.
"A written plan was located in her cell with detailed plans involving killing a female officer to obtain her keys and to utilise her finger prints in order to deceive the biometric systems.
"She was placed on the escape list, which involved the wearing of an escape suit."
One aspect of the plan was that "the finger of an officer would be cut off in an attempt to deceive the biometric security system at the prison".Dennehy was given a whole-life term after admitting the murders of Lukasz Slaboszewski, 31, Kevin Lee, 48, and John Chapman, 56, whose bodies were found in ditches in and around Peterborough in 2013.
She also pleaded guilty to two counts of attempted murder in Hereford and preventing the lawful and decent burial of her murder victims.
Dennehy, of Orton Goldhay, Peterborough, claimed at London's High Court that she has been "unfairly and unlawfully" held in segregation at HMP Bronzefield.
Hugh Southey QC argued at a hearing in March that her incarceration violated her human rights and had taken a heavy toll, leaving her "tearful and upset", and at times she was resuming her practice of self-harming.
Mr Southey described Dennehy, who was jailed in February 2014, as a "vulnerable" inmate due to her history of severe personality disorders, and episodes of self-harming dating back to childhood.
Government lawyers said the segregation was fair, justified and lawful due to the nature of Dennehy's offending and the escape risk she poses.
They submitted there was also no procedural unfairness during her continued segregation after September 2014.
Jenni Richards QC, appearing for HMP Bronzefield, described Dennehy as "arguably the most dangerous female prisoner in custody".
Dennehy "got a taste for killing" and had admitted to the psychiatrist that she was "sadistic".
Mr Southey submitted there was unfairness because the escape allegations were never properly put to Dennehy at the time.
She insisted that the alleged plot was nothing more than a "doodle" found in her diary, said Mr Southey.
The police had investigated the claims and "confirmed that no further action would be taken".
Dennehy is only the third woman to be given a whole-life prison term. Moors murderer Myra Hindley and House of Horrors serial killer Rose West are the other two.
