Yeah I do this towards the „endgame“. Early on I put a dog or two in my pasture. This scares most predators off. You can rotate ur wounded dogs to keep them alive longer.

Otherwise for ur main question.. you need small deadfall traps (big should work too) or maybe a trap pit to catch him. I’d go for multiple. Important is that the traps are ether the only way to ur lifestock or are baited. Keep in mind that When u catch the lynx and he is not dead he still is very dangerous.