Instead of writing it directly to the response stream, try the following.
Dim downloadURL As String = String.Format("window.open('download.aspx?fileID={0}','_blank','toolbar=no, location=no, directories=no, status=no, menubar=no, scrollbars=no, resizable=no, copyhistory=no, width=400, height=400');", lnkAttach.Text)
ScriptManager.RegisterClientScriptBlock(Me, Me.GetType(), "download-file", downloadURL, True)
Try this and let me know if it works.