Basically, not database and LCIA method need to be the same, but the elementary flows used in the method you select need to be used in the database. E.g., with our openLCA LCIA method pack, we reflect all different elementary flows in different databases, with few exceptions (e.g., the idea database with the original, Japanese flows is not covered in the LCIA pack but the idea database with the adapted flows; all Input/Output databases are not covered because they use an own method and very different flows). The ecoinvent database has an own method package that uses only the flows used in the ecoinvent database (and vice versa).
Hth, Andreas
