Duplicate the table, make all the fields in the new table global. Make sure the new table always has only one record.
Let the users populate the global fields and use a script to check the values and import them into the data table. That way, your user won't need editing privileges in the data table.
You can also use Manage Security to control access to records on a record by record basis. If your "lock" expression in Manage Security includes a check on a Field your Complete button modifies to mark the record "complete", it will then limit editing privileges for that one record.
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 detailed description of how to set this up.