I'd look at using Manage | Security to create a "lock" expression comparing the value of Date to the current date:
Date = Get(CurrentDate)
For all but Full Access users, this could be set up to prevent editing a record where the date in Date does not equal Get ( CurrentDate ). You'll want to also set Date to auto-enter the current date when first created so that you aren't locked out of editing a new records simply because the date field is empty.
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a description of how to set this up.