I suggest that you send them an email. In some cases "Managed by Accor" is a temporary term for a hotel that has recently been bought over and are being re-branded. In other cases it simply doesnt fit into any "category". Bothe the hotels in LP will be undergoing renovations and will be re-branded by the end of this year.

The 3 Nagas LP was recently taken over and has not yet started renovations I believe.
With so few rooms I also doubt there will be much of an upgrade.
Emails: [email protected]

Hotel de la Paix; Here too a hotel with very few rooms. Renovations here have also not yet started. It will become a Sofitel.
Email: [email protected]

Both Hotels have the same "cluster" GM: Pablo Barruti ([email protected]). I suggest you address the email to him.