Setting the background colour relies heavily on the pattern you have applied to the cell. It would be simpler to set the foreground colour instead. Since the code chooses the cell based on the location of the CC, you can treat both CCs the same way
Code:
Private Sub Document_ContentControlOnExit(ByVal aCC As ContentControl, Cancel As Boolean)
Dim StrPwd As String, iCol As Long
StrPwd = "DocumentPassword"
With aCC
Select Case .Title
Case "Lst1", "Lst2"
'MsgBox .Range.Text
Select Case .Range.Text
Case "High"
iCol = wdRed
Case "Medium"
iCol = wdYellow
Case "Low"
iCol = wdBrightGreen
Case Else
iCol = wdWhite
End Select
If ActiveDocument.ProtectionType <> wdNoProtection Then ActiveDocument.Unprotect Password:=StrPwd
.Range.Cells(1).Shading.ForegroundPatternColorIndex = iCol
ActiveDocument.Protect wdAllowOnlyFormFields, True, StrPwd
End Select
End With
End Sub