Final answer:
The fraternal society that emerged in nineteenth-century New York to serve Sicilian immigrants was the Sicilian Mafia. They provided support amidst intense discrimination and helped advance their members' interests.
Step-by-step explanation:
The fraternal society that emerged in the nineteenth-century New York as a lawful fraternal society designed to advance the interests of Sicilian immigrants was the Sicilian Mafia. During a time when Italian immigrants, particularly Sicilians, faced intense discrimination and prejudice, such organizations played a role in providing support and advancing the interests of their members. These immigrant groups, despite old country rivalries, often united to form ethnic communities and associations to protect and advance their collective interests in a new land where they were frequently marginalized.