Maybe I can do something a little different -

LCase(ThisWorkbook.FullName) returns a full path. I can change the Fullname
to simply Name.
But then LCase(file) still returns a full path. How can I change
LCase(file) to return the file name only without the path?

Dim i As Long
Dim file As Object
Dim Files As Object

FileCountOK = True
Set Files = pzFolder.Files
For Each file In Files
If LCase(file) < LCase(ThisWorkbook.FullName) Then