The Netherlands embassy in Vilnius does not issue visa.
Lithuania is part of the Schengen area. Do you have the nationality of Lithuania? Or do you have a valid Schengen visa or a residence permit for Lithuania? Then you do not need to apply for a short-stay Caribbean visa to travel to the Caribbean part of the Netherlands (Aruba, Bonaire, Curaçao, Saba, St Eustatius or St Maarten).