The principality (Fürstentum) Lübeck was part of the Grand Duchy (Grossherzogtum) of Oldenburg un 1937. Census records for the principality of Lübeck are available.
See also Kreis Oldenburg.
See 1819 census for Amt Eutin: https://sites.google.com/site/ahnensucheimamteutin/volkszaehllisten-des-amtes-eutin
Link to census database: https://aggsh.net/index.php/projekte/datenbank-volkszahlregister/das-fuerstentum-luebeck-1819