She studied Slavonic und Spanish studies at the University of Rostock and made her doctorate on literature of Latin America in 1980. Between 1969 and 1989 she worked as a teacher of foreign languages at the nautical school at Warnemünde and the Rostock University.
In September 1989 Lucyga joined the opposition party Neues Forum and in late 1989 the Social Democratic Party of Germany. She was elected as the Volkskammer delegate of Rostock in the first free election in East Germany in March 1990 and became a member of the German Bundestag after the reunification of Germany in October 1990. Lucyga was reelected in 1994, 1998, 2002 and abandoned to candidate in 2005.