Due to his unusual lightning weakness, it should be pretty obvious that the Dragonslayer Greataxe is pretty decent here. Just don't try to stagger him with it, as the axe obviously doesn't have a thrust attack (for those aiming for his hip). At 46 str/ 36dex/ 12 fth the axe's lightning call can do a pretty decent 777 dmg to him if you hit him in the right moment (it seems that bosses are more susceptible to all forms of damage if you hit them in their attack motion). Additionally, if you don't have the Irythill Straight Sword/ Rapier or don't mind getting frighteningly close, using Carthus Beacon, Pontiff's Right Eye, and Refined Claws of at least a +8 level with either gold pine resin or the frosty version of it will work very well since the left bumper series of the claws is meant to rack up combos anyways. At the same stats those claws can run up to 1700+ damage on a lothric knight (this, of course, is not Lorian; I am simply plugging for one of my favorite weapons here) without any resin and just the beacon and eye active. Oh yeah, don't try to summon help for the twin princes either as they will just get destroyed in a half-second and leave you with a buffed version of an already tough boss.