Which types of residence count fully, partially or not at all where the official rules specify this?
Lawful residence with a residence permit counts. For international protection recipients, the period from lodging the protection application to issue of the protection permit counts (unless staying in another Member State without a legal right). EU Blue Card holders may add together stays in different Member States if they have 5 years of lawful uninterrupted residence in the EU as a Blue Card holder, including 2 years in Luxembourg immediately preceding the application. Seasonal, seconded or transferred workers, students/persons in vocational training, and holders of a temporary permit with a specific limited validity cannot benefit from long-term resident status.
See recorded sources
Limits of the record- The page lists excluded categories but does not say whether earlier periods spent under those permits count partially or not at all towards the 5 years.
- https://guichet.public.lu/en/citoyens/immigration/plus-3-mois/ressortissant-tiers/sejour-5-ans/statut-resident-longue-duree-ressortissant-pays-tiers.html
For recipients of international protection, the period between the date on which the application for international protection is submitted, on the basis of which international protection has been granted, and the date on which the international protection residence permit is issued, is taken into account for the calculation of the 5-year period unless the person who was granted international protection in Luxembourg is staying in another Member State without a legal right of stay or residence in accordance with applicable national, international or European Union laws.
- https://guichet.public.lu/en/citoyens/immigration/plus-3-mois/ressortissant-tiers/sejour-5-ans/statut-resident-longue-duree-ressortissant-pays-tiers.html
Holders of an 'EU Blue Card' residence permit are allowed to add together their stays in different Member States in order to satisfy the requirements regarding duration of stay, if all of the following conditions are met:
5 years of lawful and uninterrupted residence in the European Union as an EU Blue Card holder;
2 years of lawful and uninterrupted residence in the country, immediately preceding the submission of an application for long-term EU resident status, as a holder of an EU Blue Card.
- https://guichet.public.lu/en/citoyens/immigration/plus-3-mois/ressortissant-tiers/sejour-5-ans/statut-resident-longue-duree-ressortissant-pays-tiers.html
The following third-country nationals staying in Luxembourg may not benefit from long-term resident status:
seasonal, seconded or transferred workers;
student or person registered in vocational training programmes;
person holding a temporary resident permit with a specific limited validity.
- https://guichet.public.lu/en/citoyens/immigration/plus-3-mois/ressortissant-tiers/sejour-5-ans/statut-resident-longue-duree-ressortissant-pays-tiers.html
Please note that these provisions are not applicable to third-country nationals who are family members of an EU national (or of nationals of a country treated as such). Such persons may, after a 5-year stay with the EU national in Luxembourg, apply for a permanent residence permit for a family member of an EU citizen.