Say I have a blood angel character with the artisan of war warlord trait (+1 to the damage characteristic of one of his weapons) and TWO lightning claws.
The warlord trait only applies to one weapon, so presumably this means only one of those lightning claws does extra damage.
Does this mean my extra attack for the second lightning claw will only do 1 damage?
Artisan of War: Add 1 to the Damage characteristic of one weapon carried by your Warlord.
Lightning Claw: You can re-roll failed wound rolls for this weapon. If a model is armed with two lightning claws, each time it fights it can make 1 additional attack with them.
I would say the extra attack can be made with either claw, as it says "them" rather than "this weapon" or "the second claw".
Thus, you would make an extra attack and it would also be +1 damage, because you pick the blinged out claw.
Of course you could also argue "with them" means you get one additional attack per claw, for a total of 2, but that's just sillyness! Seems to be a poor phrasing since you're generally going to only pick one weapon to use in the fight phase, no need to split between the two.