Hi,
The date field is saved to the DB in ISO8601 format and the cascading dropdown reads this value and not the formatted date that is presented when you render the item in the form.
To format the date like you want you must create a new calculated column in the list with a formula like this:
=TEXT([YOUR_DATE_FIELD],"MM/dd/yyyy")
And then use this new field in the Comma separated list of fields in the lookup list textarea.
Alexander