no in my opinion it wouldn't be interesting. Those lynx take down reindeer and Roe deer, their main quarry. Their claws are massive. I'm sure a game dog could kill a lynx, but not after a long ordeal of being ripped to shreds, and it would probably die later from it's horrific injuries. This is why they use and bred baying hounds to hunt the lynx and bear in their country.
what about dogo argentino's, american bulldogs (Painter lines), Rhodesian Ridgebacks etc? I read an account of a German Shepherd killing a Canadian Lynx after it tried ambushing it without to many scratches.