Once you deplete half his health bar, Lorian starts to get a bit more aggressive. He’ll imbue his sword with magic, and start teleporting far away from you. When he reappears, he’ll occasionally swing the white magic sword downwards, sending a shockwave across the room. You’ll want to rotate the camera to look out for him, and roll to the side right before he slams the sword down.
When you’ve depleted his entire health bar, Lothric himself will enter the fight and revive Lorian. Now, Lothric will be on Lorian’s back as he casts magic spells at you. Lorian’s move set will remain the same, but you’ll have to start watching out for Lothric’s homing magic projectiles. Just like the fight with Aldrich, the smaller projectiles can be avoided by sprinting or rolling away. He also has an attack where he launches a large magic spear at you. This attack will not home in on your position, but it deals a significant amount of damage.
Your goal in this phase is to attack Lothric. Aim for Lorian’s back and you should be able to damage both of them. Lorian will have significantly lesser health here, so if you can deplete his health bar, Lothric will take time to revive him, leaving him open to attacks. Once you’ve defeated Lothric, take out Lorian if he’s still alive, and the fight is yours.
Be sure to check out our Dark Souls III wiki for more tips and tricks.