Visas to Latvia for citizens of Schengen Agreement member states (also Belgium and Luxembourg) are not necessary. For travelling, they need a valid passport or national identity card.
Each Schengen Agreement member state decides on its own, which documents (residence permits) issued by it, are acceptable for travelling to other member states. Information on these documents is included in Annex 4 List of documents entitling holders to entry without a visa of the instructions Common consular instructions on visas for the diplomatic missions and consular posts (see the web site The access to European Union law). Should it be not clear, whether a specific document grants such rights, one should consult the immigration institutions of his home state.
For Luxembourg: Ministère des Affaires Etrangères et de l'Immigration - Service des étrangers, Hôtel Saint Maximin, 5 rue Notre-Dame, L-2240 Luxembourg; Tél: +352 (0) 247-84040; +352 (0) 2478-2478; web: www.mae.lu.
More information on entry of foreigners into Latvia is available here: http://www.am.gov.lv/en/service/entry-into-latvia/.
More information on travelling with residence permits issued by Schengen area states is available here: http://www.am.gov.lv/en/service/entry-into-latvia/visiting-latvia/travel-rp/.