Lich bane, Duskblade, Stormraor combination?

Just a random thought. ive been playing some akali, and it's dumb yes i know, but im just curious and playing around with builds. if i built Lich Bane, Duskblade, and Stormrazor on akali (along with gunblade, zhonyas and sorc shoes), and i Q or E, break the ring and then W, and wait 1.3 seconds in the shroud, and AA would A) Lich bane proc cuz of sheen B )Duskblade proc because i was invisible for 1 seconds and C) stormrazor proc because i havent attacked in the last 1.3 seconds.

im curious as to the interaction between these items, and wondering if they would all proc off of that AA passive, or if riot realized this, and there's limits, and if so, which 2 items would be best with each other? like i said it's just a thought and it just got me very curous