In the EU, the country responsible for your social security, including your health insurance, depends on your economic status and your place of residence – not your citizenship.
If you are moving your residence abroad on a permanent basis it might happen that you will be no longer entitled to medical treatment in Lithuania and will be no longer entitled to use your Lithuanian European Health Insurance Card to access healthcare abroad.
Before leaving to your new destination it's important to check what health services will be available to you in that country. Healthcare systems vary from country to country and might not include some services that you would expect to get free of charge in Lithuania.
In order to find out more about your rights to get healthcare services, unemployment benefits and other social security benefits you should check Country by Country guide at European Commissions website:
However, if you reside in other EU Member State, Norway, Island, Lichtenstein or Switzerland and receive Lithuanian State Social Insurance Pension or still continue working in Lithuania you might be entitled to healthcare on behalf of Lithuania. In order to ascertain you rights, please, turn to the nearest Territorial Health Insurance Fund (THIF). If you have a right to receive healthcare in the country of residence on behalf of Lithuania the THIF will issue you a relevant E form (E106, E109, E120 or E121) or a portable document S1. You shall register this document with the relevant authorities abroad in the country of residence. After that you and your family will have the same medical coverage as residents of that particular country.