Ms McKee was shot dead by a New IRA gunman while observing a riot in Derry on Thursday, April 18.
Nichola Corner told BBC Radio Foyle there are no words to describe what it had been like for the family since her death.
They felt no closer to knowing who killed the 29-year-old north Belfast woman, she said.
In an interview with BBC Radio Foyle’s reporter Teresa Craig, Mrs Corner said: “It’s like living in a nightmare that you just can’t wake up from.
“Horrific, to say the least.”
On the night of the murder, Mrs Corner said the family initially believed Ms McKee’s injuries were not life-threatening.
“I got a phone call to say that Lyra had been injured, hit in the head, and police had taken her to hospital,” she said.
“I actually thought she’d maybe been hit by a bottle, a brick or some kind of object of that nature.”
After some time spent waiting for more detailed information, Mrs Corner decided to call Lyra’s phone, expecting her sister to answer.
“I said: ‘Are you alright wee love? Have you been seen by the doctor yet?’
“[I was] expecting it to be her, but obviously it wasn’t her.“That’s when I was told that she was very seriously injured and the emergency personnel were working on her at the hospital and I couldn’t understand why.”
In a further phone call, Mrs Corner was told her sister had been shot.
“You can imagine the devastation of hearing that news, that she had been shot in the head,” she said.
“My husband had to pull over because I was screaming and couldn’t breathe.”
While she was telling her mother and other family members about the shooting, she received another call from a PSNI constable, who told her police would collect the family to bring them to Altnagelvin Hospital in Derry.
The officer told her Lyra had died.
“I was actually still in my street. Mummy was still in the car. My whole soul just left.”
When she eventually saw Lyra, Mrs Corner said “it didn’t register” that she was dead.
“She looked just like she was sleeping.”
Three months on, Mrs Corner said there is “still part of you that’s not quite believing it to be true, because it is so unbelievable”.
Mrs Corner has previously offered to meet her sister’s killer and support him in “accepting responsibility for your actions”.She again appealed for anyone with information on the killing in Derry’s Creggan estate to come forward.
Mrs Corner said her family found the media coverage around her late sister’s death at times difficult to deal with.
“My mummy does feel that people have been treating her daughter as public property and she wants to ask people to stop doing that, she wants to reclaim her daughter,” she said.
Two men have been charged with rioting in the city on the night that Ms McKee was murdered.
A 57-year-old woman along with an 18-year-old man and a 15-year-old boy, who were arrested in the aftermath by detectives investigating Ms McKee’s death, were released without charge.
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