After Lithuania joined the European Union (2004) it also ascended to its Schengen Treaty. This treaty establishes a single Schengen visa to enter all the member states. Within the Schengen area, there are no customs nor border control meaning that you could easily combine a trip to Lithuania with some neighboring countries (Latvia, Poland).
One may apply for a Schengen visa at any Lithuanian embassy or consulate. Furthermore, if there is no Lithuanian embassy or consulate at your country, Lithuania is represented by an embassy or consulate of some other EU-member state; a visa could be applied for there.
While Lithuania would be willing to extend visa-free regime to more countries the Schengen regime means that Lithuanian visa regime has to be similar to that of Western Europe (which is plagued by illegal immigration and therefore is reluctant to grant visa-free regime to most countries except for the richest ones). Japan, South Korea, Taiwan, Malaysia, UAE, Brunei, Hong Kong, Israel, Macau, Australia, New Zealand, USA, Canada and most of Latin America are the only areas outside Europe whose citizens could travel visa-free to Lithuania. On the other hand, nearly all Europeans can do this with the exception of Russian, Ukrainian, Belarusian and Turkish citizens.
Schengen visas are short-term only; a longer visa is called "national" (and must be applied at Lithuanian embassies/consulates) but still allows traveling inside all Schengen area. If you are just transferring at the airport you need no visa unless you come from a migration-sensitive country (some Asian and African countries).