Whenever he raises his arm for the ground slam + fire AoE, I just chuck my Accursed Brew at his face. With good arcane scaling, it can take out close to 900 of his HP, plus it opens him up for a visceral on the spot. As for weapons, the Whirligig Saw is ideal, since he's still a beast and therefore weak to serration, and the blunt nature of the weapon seems to help with breaking limbs.
Overall, the fight necessitates that you memorize each and every one of his attack animations, the most important discrepancy being between his walking series of southpaws, his most common attack patterns. If he keeps his left arm (the smaller, less hairy, inanimate arm) off the ground, stay back and wait for him to raise his large claw for the fifth swing, at which point you should dash in and strike just as the attack ends, likely hitting either his attacking arm or his face. If the left arm IS on the ground, he's going to belly-flop and lunge, which has incredible range and tracking. In this case, you'll want to dodge through the attack and to the right, playing limbo with his attacking arm, then beat his *** quite literally for one whole second before dodging back to avoid his revenge swipe.
Probably the most lethal attack is his surprise belly-flop, which doesn't have much in the way of a warning animation and can easily one-shot players on NG+3 and above. Laurence leaps forward and completely stretches out his legs and his long arm, landing flat on his stomach to maximize his range, possibly turning the entire length of the cathedral into one giant hitbox. I would say to dodge to the right, but the attack is so quick, you'll probably get squished anyway. I've managed to dodge and get hit just by his foot, where you'd imagine the least of his weight to be distributed, but even that manages to obliterate me at full health. Thankfully he only does this attack very rarely, but god damn is it nigh-impossible to avoid.
For the final phase, wait for him to start his crawling attack, and carefully dodge inward to the left side, behind his smaller arm. He struggles to turn while doing this attack, so simply keep close to his side while avoiding his anterior attacks and his posterior secretions (ew lol), and when he calms down, give him one good whack before retreating, as he'll probably pull a circular swing. Again, if he raises his arm for a ground slam, get back immediately, because he's still got his near-perfect tracking despite having no legs. Rush in and aim for his head after each attack. Mind that if you linger for a combo, he'll probably swipe without warning and potentially one-shot you, as always.