Unionist leaders need to give the chief constable “space and time, but also support” to build confidence in policing, Justice Minister Naomi Long has said.
It followed the publication of a review into policing in south Armagh.
DUP leader Sir Jeffrey Donaldson said Mr Lyons spoke for his party, however, he refused to directly repeat the call.
The TUV has also called for Mr Byrne’s resignation.
Mrs Long said there had been no consultation with the Department of Justice about what the Police Service of Northern Ireland (PSNI) recommendations would be.
But the justice minister said other political parties should “move back” from calls for Mr Byrne to resign.
“What inroads have unionists made to assuage concerns and build confidence in communities? It’s not just the responsibility of the PSNI and me,” she said.