@ 97BligenN, Lich Bane is indeed a great choice because of Mark of the Assassin.

To the guide, I wouldn't call Spirit Visage a core items because you mainly purchase offense options as core items on Akali. As a good choice I suggest you to weight Zhonya's Hourglass more and adding it to the final build. Liandry's Torment is a poor option and items like Deathfire Grasp or Rylai's Crystal Scepter are way better.
When using that much points in the offense Mastery tree you should consider Block over Recovery but I thnik going for 21/9/0 is anyhow better. Leaving out Masteries like Warlord can help you to selecting your points in AD and AP Masteries.

go mresist blues instead, akali is too squishy imo
why does full build have 5items?
also rylai is pretty much a must, as it gives decent ap, sticking potential and survivability
abyssal scepter is a very good item for akali since she's always melee range
warmog's is never good because of the botrk
lich bane isn't a good choice since when bursting you do Q->R->Q->E->R, but I guess it can be used
You took no cdr in masteries and so much ad? Not rly... best, better get extra tankiness
didn't watch the video but wtf that vid in the matchups?
also no c2v