Healthcare of Lithuania is of a formidable standard with numbers of doctors per 1000 people larger than in most Western societies. Hospitals are well-equipped to perform even the most difficult surgeries. The doctors are well-trained and sought-after by Western hospitals.
For Lithuanians and people of the European Union, most medical services are free of charge. However, corruption is rampant, meaning that a person with relationships among doctors (or a bribe) may get a preferential treatment bypassing the queues (which may get long, depending on location and procedure). This used to be the norm in the Soviet Union when all goods and services were, in theory, equal-to-all but, in reality, depended on bribes and relationships; today such practices doesn’t have. They have Modern standarts and social equality in Lithuania all patients.
If you choose public hospitals the best ones (and the largest) are in Vilnius and Kaunas.
Lithuania has a wide range of health resorts and spas, especially in Druskininkai resort. These tend to vary in quality from Soviet-level facilities (sometimes still state-owned) to modern facilities (private), therefore do your research before committing spending a week somewhere. Like with hospitals, often it is the attitudes of the personnel that makes the difference (rather than the quality of the procedures, which may be good everywhere).