You should be able to set a condition somewhere to change the value of the Completed field to Yes under conditions you specify. When would you run this process? Is it determined by date, or some other action?
As to locking the records, on the On Current event of a form, you can set the condition that if Completed = True then Allow Edits = False.
You can also prevent users from viewing completed records in your data entry form by filtering for Completed = False, and then have another form for viewing completed records, or use reports instead.