Visa applications are handled by the Consulate General of Italy in Lagos, whose website https://conslagos.esteri.it/en/ provides all relevant details.
Please note that visa applications must be submitted through the TLSContact agency, which has submission offices in both Abuja and Lagos. Appointments must be booked in advance, following user registration, via the website https://it.tlscontact.com/ng/splash.php
All general information regarding the submission of visa applications for Italy and the Schengen Area is available on the official website of the Ministry of Foreign Affairs and International Cooperation (MAECI): Visa for Italy