Locking a Field Once populated

Set up a field called [Record ID# mirror]
With a formula of simply [Record ID#]

(  for some reason, form rules do not let you use the record ID field directly. )

Then make a dynamic form rule

When  multiple conditions are true

When [Record ID# mirror] not equals (blank)
Users is not in the Role High Level

Make read only [Project Completion Date]

 In other words, what is happening here is that before the record is initially saved, the record ID does not exist so it is blank. Under those conditions you were OK to let anybody enter a project completion date. But once the record has been initially saved once and a record ID number has been assigned then the normal lower level role permission users are not allowed to edit that field.

Many thanks Mark.  I used this solution of yours in relation to another issue,.  So I have a field in place.  Great innovation.

Mark, in case where record was saved, however, the field in question was left blank or the info was not available at that time and the field is now read only using this solution. How could I ensure that user is able to edit one time using this solution as long as the field is blank?  

No problem,
change the form rule

when multiple conditions are true
when ALL of the following are true

Date is not equal to (leave blank)
[Record Id# mirror] is not Equal to blank

Make read only [Project Completion Date] 

very kind of you for your help.  This worked well.