Authorities in the North want to prosecute the 44-year-old, from Malahide Road on the capital's northside for Lawlor's assassination in Belfast on April 4, 2020.
The complaints relate to concerns about the standard of the investigation, including its management and direction, the conduct of the investigation team, and their engagement with the victims.
Linda Costello was found with serious injuries at a home in Graigucullen, Co Carlow, and was rushed to St. Luke's General Hospital for treatment. She later died on April 10, two weeks after the incident.
The industrious buzz of bees tackling the dregs of cherry blossom was lawnmower-loud, accompanied by back off peeps from blackbirds nesting in the ivy.
Hundreds of gardaí have formed an effective ring of steel around the city centre. Protesters did not resist the move to free up the country's main thoroughfare.
The whole family is distraught but while grieving for their eldest child they are living in fear for their lives at the moment. They haven't been able to leave the house since.
Kimberly Milne's tragic death highlights a disturbing trend where victims of domestic abuse are more likely to die by suicide than be killed by their partners, raising serious concerns about accountability for alleged abusers.
I called my son Finbar because I knew he was going to become famous and wanted him to have a name that everyone would know. I never thought it would be on the front pages because of his own murder.
