In New York, a lender cannot repossess your car *solely* because you lack insurance. Repossession is typically allowed only if you're in default on your loan payments. While lack of insurance might be a violation of your loan agreement, it's not an automatic trigger for repossession. The lender would generally need to provide you with notice and an opportunity to cure the default (e.g., by making payments or obtaining insurance).
However, the lender *could* repossess your car if your lack of insurance is considered a breach of contract that leads to a default on your loan. Many loan agreements require maintaining insurance as a condition of the loan. Failing to do so could be interpreted as a breach, leading to the lender declaring you in default and initiating repossession. The specifics depend on the wording of your loan contract.
