You can't do this using the out of the box controls. You will need to use a
custom Field control for the site  columns in your content  types that you want to
cascade. Check out the following Codeplex project for some custom Field types
that will work.

http://www.codeplex.com/CustomFieldControls

You can achieve this by using CAML query, when you are using custom
asp.net pages. But I am not sure on how to achieve this through custom
content types. once you get any solution for this, do let me know.

The only way I know of is to create  custom field types. The following link may
include what you are looking for:

datacogs.com/datablogs/archive/2007/08/26/641.aspx

The code is offered to this solution. Use it, because there may be some minor
bugs that may require debugging. I used this to develop a "Grandchild dropdown"
so it goes 3 levels deep in its filtering.

Also, there's a quirk in this solution if you you use this CFT in development
and then deploy it as a list  template or site  template to production. In
production, you will have to go into the list settings for each field that uses
this CFT and verify its properties. This is because the development URL for the
dropdown list will be different that the production URL.

This is a lot to swallow, but the CFT is really cool to use.

This work on webpart. How do I get it to work with content  type. I'm attaching
a content type  that have these lookup list  to a document  library. So when I
click NEW from the document library  menu, Office 2007 open with the Document
Information Panel. This DIP will have metadata including my three dropdown
list. This is where i want it to be able to filter. Any idea?