It's possible to lock them as specified. You will need an auto-entered TimeStamp that enters the creation date and time and this appears to be the case.
Then you can set up a "lock expression" in the data entry users' privilege set such as:
( Get ( CurrentTimeStamp ) - CreationTimeStampField ) / 60 < nn
replacing "nn" with the desired number of minutes.
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.
Thankyou for your response PhilModJunk.
I made a copy of the test database
With [Full Access ] I went in and applied that formula change (inserting our field name in lieu of CreationTimeStampField) to the [Data Entry Only] Privilege Set.
The result is that it appears to lock the existing record in the portal immediately and it also appears now the portal is locked totally and prevented me as a [Data Entry Operator] from adding any new records to the portal.
I closed the database and re-logged in with [Full Access] and reversed out the change and removed all limiting controls from the record and its fields.
On accessing the portal even [Full Access] now can't delete records or add records to that portal - it is totally locked from change by any user even though there are no controls in "security" on the applicable record.
I will make another copy of the test database in the next day or so when I get the time and try and find out where I went wrong or if the problem is replicated again.
If you really have the database file open as a full access user, any settings in the privilege set used with another account will not have any effect on what you can or cannot do with the database.