A few games ago in patch 7.20 I went alkali with this build and went 20/1/3 in 20 minutes because they FF so... could be my low silver elo, but definitely viable if their team is really squishy and youre ahead!

About the lich bane you have included in your build, I don't care who you see doing it whether it's a pro or even just professor akali, lich bane is not good for akali anymore do to her rework and it shouldn't be used it is just wasted and doesn't even help that much when you could be getting other items that do more damage, i know that professor akali is a very good player in league and that's what most people want to be good, that's why they watch bigger people to see what they do, you should be building off of experience and what works best for you, not what other people do, so I hope that I helped you understand even if you don't take my advice, have a nice day.