Historically when Cotroni created the family it had no LCN background, it was just an Italian organized crime family that controlled the city of Montreal. Also being from Calabria I don't think they had any 'Ndrangheta connections either. So it was not until the Bonnanos came up that they entered the American LCN circles.

Overall I consider them a mafia family with LCN elements and connections, but not exactly LCN themselves since they're no longer part of the Bonnano family. They also had Sicilian LCN connections through the Rizzutos. I'm not sure if Nick Rizzuto Sr was a made guy back in Sicily but he did marry a woman who came from a mafia family.