Depends on how you're playing her. Honestly I find Lich Bane to be a very niche item choice. It all depends on whether or not you can get in and half the time the most you can really do is Q and R which is all you need sometimes.
Just the little 200 or so AP from this build alone is enough to burst a squishy, you don't need much more so might as well spec into survivability.
That's my experience anyway, there's just a point where I feel I don't need any more damage.
Also Rylais helps your team catch up, because half the time you aren't gonna be able to pull off the job alone. The charm isn't super reliable to land so having Rylais definitely helps especially when charm is on CD.
That and in top lane Rylais tends to dick on a few melees.
Also why I don't take Sorc Shoes, just don't need em.
I tried out Lich and Ludens, both seemed to not help that much in burst.
In any case, you build items for 2 reasons: to enhance your strengths or compensate your weaknesses. In this case I'm shooting for the latter.