The lions were among those who ate the remains of a young male giraffe killed by the same zoo last month because of "inbreeding", Xinhua quoted Copenhagen Post as saying.
This time "the generation shift" brought the end to the lives of a 16-year-old male lion, a lioness of nearly the same age, and two younger females.
'Lions were killed to avoid inbreeding between young lions and their father'
Media around the world responded critically when the Copenhagen Zoo dissected the 18-month-old giraffe named Marius in front of school children in February, but the zoo doesn't fear a similar uproar after killing the lions.
"I think people are more enlightened after Marius," said Steffen Straede, head of the zoo.
"Marius hasn't made us the least bit afraid, because what we are doing is the most correct thing to do."
Straede maintained that the lions had to be destroyed also partly to avoid inbreeding between the two young lions and their father.
He said a new three-year-old lion male will be introduced to the family in a few days.
Last month, regardless of sharp reaction by animal rights and social media commentators the zoo put down Marius as planned in accordance with the zoo's policy on in-breeding.
"The zoos have produced him so it is their responsibility to find him a home, no matter how long it takes. They must not be allowed to take the easy option," argued Maria Evans, an animal protection activist.
The zoo said it had taken the decision to kill the young and strong Marius and feed him to some of his fellow animals in order to keep the giraffe population "genetically sound".
"You must do what you have to choose and make sure the animals you keep are the ones with the best genes," said Bengt Holst, the scientific director at the zoo, explaining the killing.