Yes, your spouse can apply for a residence permit on the basis of family reunification. Amendments to the Immigration Law of Latvia at the moment do not really allow Russians to apply for a residence permit, but this prohibition applies to part 1 of Article 23 of the Immigration Law (which specifies all the basis for applying for a residence permit – from employment to investment), but it does NOT apply to part 4 of this article, which deals with family reunification. Thus, a Russian citizen cannot obtain a primary residence permit as an investor, employee, student, member of the board, etc., but it is possible to obtain as a spouse of the holder of a valid residence permit.