Police were attacked with petrol bombs and masonry at the City Cemetery following Monday’s parade.
Vigils had been held earlier to mark the third anniversary of Lyra’s death in Derry and Belfast.
“All we wanted to do was to pay tribute to our precious Lyra,” Nichola McKee Corner said.
Speaking to BBC Radio Foyle, Mrs Corner said she had sympathy with the people of Derry “for having to put up with these people who deliberately orchestrate violence”.
“I believe, to tell you the truth, that these people deliberately orchestrated this violence to take media attention away from the fact it was Lyra’s anniversary,” she said.
“They piggy-backed on the media attention that it would bring to the city and it’s unforgiveable.”
Ms McKee was shot dead while observing rioting at Fanad Drive in the city’s Creggan area on 18 April 2019.
The New IRA said its members were responsible.
Three men have been charged with murder and another six charged with rioting and public order offences on the night Ms McKee was killed.
The parade on Monday had been planned by the National Republican Commemoration Committee.
It organises events on behalf of the anti-agreement republican party Saoradh, the political wing of the New IRA.
About 1,000 people took part in the demonstration; some of them with their faces covered.
Police came under attack at the City Cemetery following the parade.
Seven men arrested under the Terrorism Act have since been released pending reports to the Public Prosecution Service.
A 40-year-old man, who was arrested on suspicion of disorderly behaviour and resisting police, has since been charged.
On Tuesday, Derry’s police commander Chief Supt Ryan Henderson described Monday’s disorder as “premediated”.
He said that “young people were used, encouraged and cheered along by adults to attack the police”.
Mrs Corner said her sister “would be horrified” that young people were being used in that way.
“It amounts to abuse, it’s shameful and it’s absolutely disgusting,” she said.
“These young people are being groomed and being manipulated by older people to do their bidding.
“Adults who encourage young people to engage in violence should be charged with child exploitation,” Mrs Corner added.
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