What are your thoughts? I was thinking Boots + 3 Pots -> Dorans x2 -> Sheen -> Sorc Boots -> Rylai's -> Lich Bane -> Deathcap.

It might be a huge investment and take too long to set up, however... And I'm personally horribad at last hitting creeps.

The reasoning behind Lich Bane is because of the nerf to Ahri's dash. With a huge second in between - and with relatively long cooldowns - a beefed up autoattack seems kind of worth it, right?

sheen early on will heavily delay your damage from other item, Ahri also want some spell vamp for sustain, and finally you want a deathcap before lichbane as there isn't enough AP to make lich bane worth the cost if you don't have enough AP

I use Lich bane on her, but as a late item if game lasts that long.
I am also pondering about the effectiveness of Rilay. I love it, but all her spells are area spells, meaning Rilay slow will be weaker. I am considering swapping it for RoA, and Catalyst will provide good sustain early. Possible more than Spell Vamp as, again, due to her area spells, the effect is weaker (and you have it from her passive with good frequency if you have good aim).

Much as is the case with most mages, Lichbane works as a luxury item if you wish to get one, but it's not necessary (great for taking towers, but you'll have to stop and auto in a fight which you may or may not want to do)

There are only two AP mid that get lich bane rather early, first one is TF, the second one is Sion.

They both get it after deathcap, however.

You get Lichbane on Ahri because it has MR, bonus movement speed and AP. That is, you want to build Ahri tanky but still scale your ability to do damage.

RoA --> Merc Treads --> Rylai's --> Abyssal Scepter --> Lichbane --> (Optional Item)

The combination of bonus health from RoA and Rylai's combined with slows, movement speed, Tenacity and MR make you a kiting AP bruiser that's incredibly difficult to pin down and kill. The damage proc is just a pleasant extra that adds to your harassment and burst.

Don't chase the Ahri.