The 29-year-old journalist was shot in the head by dissident republican group the New IRA while observing clashes with police in Londonderry in April.
On Thursday, a 46-year-old man was arrested by police following a number of searches.
He was arrested under the Terrorism Act and has been taken to Musgrave Serious Crime Suite for questioning.
The Police Service of Northern Ireland's Major Investigation Team carried out searches at properties in the Northland Road and Creggan areas of Derry on Thursday morning.
A number of items were also seized and taken for further examination.
Detective Superintendent Jason Murphy has made a fresh appeal for information to help the investigation.
"Since Lyra was murdered following violent disorder in Creggan in Derry/Londonderry on 18th April, our investigation has received widespread support from the community," he said.
"I still want to hear from anyone who has any information and would appeal to the public to contact my team of detectives on 101."