Belfast City Council confirmed the 7-year-old dog, a pit-bull terrier type, was put down after a deadline for legal appeals expired.
"Whilst there is an exemption scheme to which dogs of this type (pit-bull terrier type) may be admitted as an alternative to destruction, there were no such measures that could be applied in this case that would address the concerns relating to public safety," the council said in a statement.
"The council's expert described the dog as one of the most unpredictable and dangerous dogs he had come across.
"The council regrets that the court action was necessary but would emphasise that the safety of the public remains its key priority."
Pit bulls and dogs like them are illegal in Northern Ireland.
Lennox was impounded by Belfast City Council's dog wardens in 2010. He was assessed to be a danger to the public and subsequently ordered to be put down.
His owner, Caroline Barnes, who is disabled, argued he has never bitten anyone and is not a risk, and embarked on a lengthy legal wrangle to have Lennox spared.
In June, Northern Ireland's most senior judges rejected Barnes' legal bid to overturn an order for the destruction of her pet.
Her battle for Lennox became an international campaign to save his life. It went "viral" on social media websites and attracted tens of thousands of well-wishers. Campaigners claimed to have attracted 200,000 signatures in support of a reprieve for Lennox.
Two lower courts had already ruled that the dog should be put down.
Some of the dog's followers took the campaign to extremes and Belfast council workers became the focus of intimidation and abuse.
Last year, threatening letters, one drenched in petrol, were put through the letter-boxes of two female dog wardens.
