I've found a quick way to end Lynels without using durability. First, shoot them in the face, then attack with the Master Sword, hop on their back and attack with your best weapon. (when riding Lynels your weapons don't take damage) This also works a lot faster with barbarian armour or an attack...
I've found that if you use the Lynel mask (from Kilton), you can get close and get a few extra hits, although the stronger Lynels do realise you're an imposter very quickly.