It was back using HG before the patch. Liandry's Torment considered a late game item for Ahri but I find sticking to Void Staff and Rylis much better since I don't really feel Ahri needs to rush Liandry's Torment because she already has strong burst. Though everyone has different play styles, maybe Liandry's Torment actually works well for you.
The builds depend. If your team has plenty of movement disruption and enemy team is lacking magic resist, Liandry's Torment health, magic penetration, 70 ability power, and a damage over time gives ability power caster more survivability and punishes them if the battle drags out. If the enemy is stacking magic resist, Void Staff and Abyssal Scepter should do the work.
Yeah builds usually ending up different depends on how the team is doing and who are on the enemies team. Supposedly in that sense there would be some reasons to make different items. Think Liandry's Torment is always an arguable item for Ahri since some players prefer different styles. Usually I play Ahri purly as glass cannon, only item that actually adding health was Rylis.
Never really got the hang of using Death's grasp, how does that active work?
Since Ahri unlike many other AP casters have to get into the fray, she can choose one target to tag with Deathfire Grasp to nuke someone like no tomorrow. I think its great with the hidden amplify damage, ability power, and cooldown. I usually build Deathfire Grasp on her and out of half my wins (out of 600) are from Ahri with DFG. You should try it!