Check if there is a change in cell

.
Gotcha !

There are several things you will need to do to accomplish your goal.

In the ThisWorkbook module, you can place this macro :

Private Sub Workbook_BeforeClose(Cancel As Boolean)

	'The name of your macro
	SaveOrNotMacro

    	Application.DisplayAlerts = False
  
    	Application.Quit

End Sub

The SaveOrNotMacro (or any other name you like) is the macro you will create in a Regular Module. This macro will give the user the opportunity to
save or not save the changes made .... when they close the workbook.

The macro will have similar logic from your posted macro :

Sub SaveOrNot ()
Dim LRsp As Long

Beep
        LRsp = MsgBox("Do you want to Save Changes made? ", vbQuestion + vbYesNo, "CHANGES")

        If LRsp = vbYes Then
          	UpdateLogRecord
        Else
		'leave this area blank as it will cause the logic to go straight to the
		'Workbook_BeforeClose event ... closing the workbook without saving.
        End If
End Sub

I haven't tested the above macro here. There may be some required changes.