wallertown, the page you are quoting might not be up to date. For example, they still don't list any lounge for TLS, while AF pax in TLS are allowed to access the airport lounge.
As Goldorak said, we would enjoy a first-hand experience that could testify which information is the right one. So feel free to try And expect the worst case scenario of enjoying the lounge alone, it will still be a great experience.