Lich Bane on Cassio

Why isn't this built more often? Cassio's AP ratios are pretty shitty, so the pure AP build really isn't that good on her; For this reason, wouldn't Lich Bane be a perfect item on her? She's often going to be attacking from auto attack range because it's almost the same range as her E. Her low cooldowns mean she can proc LB on cooldown. The extra move speed is always good, too. It could fit into this build like this: Seraph's/ Abyssal/ Sorc Shoes/ Zhonya's/ Lich Bane/ Void Staff.