If you use the Blade of Mercy trait to do nonlethal damage with a lethal weapon (like a greatsword) at no penalty, is the precision damage from a sneak attack lethal or nonlethal?
Blade of Mercy:
When striking to inflict nonlethal damage with any slashing weapon, you do not take the normal –4 penalty on your attack roll, and gain a +1 trait bonus to any nonlethal damage you inflict with a slashing weapon.
Sneak Attack:
With a weapon that deals nonlethal damage (like a sap, whip, or an unarmed strike), a rogue can make a sneak attack that deals nonlethal damage instead of lethal damage. She cannot use a weapon that deals lethal damage to deal nonlethal damage in a sneak attack, not even with the usual –4 penalty.
Blade of Mercy only removes the penalty for doing non-lethal damage. It doesn't make the weapon a nonlethal weapon, which is required to do nonlethal damage with sneak attack.
So by RAW I believe it would be lethal damage.