According to the explanation by its constitutional court, Lithuania is a democratic parliamentary republic with elements of a semi-presidential republic. This means the parliament “Seimas” is the most powerful institution and the government is selected by the parliament. Seimas is elected by two different systems: 70 seats elected by proportional representation akin to the Italian system and the remaining 71 are elected in separate constituencies similarly to the British or US parliament.
The president (directly elected) is always a moral authority and his or her popularity almost never drops below 50% whoever he or she would be. Perhaps this is so because the president has little real power so any shortcomings could be easily blamed on the government or the parliament (these two institutions are always unpopular, whichever party would be in power).
60 municipalities (population 4000 to 550000) are Lithuania's primary administrative divisions; their directly-elected councils and mayors are responsible for local affairs. Lithuania is not a federation, however, so municipal powers are limited.
All other institutions (among them whole judiciary) are appointed rather than elected. Referendums are rare.
Scheme of how Lithuanian institutions are elected / appointed: