** Shares of medical device maker LivaNova LIVN.O rise 3.2% to $40.49

** Italian Supreme Court has ruled that LIVN is responsible for about 333 million euros ($363 million) of environmental liabilities, which will be recorded as a liability in Q1 2025 - SEC filing

** Co is tied to a 454 million euro environmental liability case linked to SNIA, a former parent of Sorin, which merged with LIVN

** Supreme Court's decision shortened LIVN's liability by 121 million euros, and the case will now return to the Court of Appeal of Milan to determine costs and damages

** LivaNova did not immediately respond to a Reuters request for comment

($1 = 0.9173 euros)

(Reporting by Kamal Choudhury in Bengaluru)

((Kamal.Choudhury@thomsonreuters.com;))