Libya Stabilization Act This bill provides for sanctions and aid related to the conflict in Libya. The bill provides statutory authority for an April 19, 2016, executive order imposing property- and visa-blocking sanctions on persons contributing to the violence in Libya. The President shall impose property- and visa-blocking sanctions on any foreign person that (1) knowingly supports or engages in a significant transaction with a foreign person knowingly operating in Libya on behalf of Russia in a military capacity, (2) engages in significant actions threatening peace or stability in Libya, (3) misappropriates Libyan state assets or natural resources, or (4) is knowingly responsible for or complicit in serious human rights abuses in Libya. Such sanctions shall expire on December 31, 2024. The U.S. Agency for International Development may provide humanitarian assistance to individuals and communities in Libya, including urgently needed health assistance, food, and shelter. The Department of State shall work to strengthen Libya's democratic governance, including by providing assistance to (1) unify Libya's financial and governing institutions, and (2) ensure transparent and credible future elections in Libya. The Department of the Treasury shall vote and argue for international financial institutions to support an economic recovery in Libya that complements the establishment of democratic institutions and rule of law.