Bahn.de seems to show only the through trains to Moscow which run from Kaliningrad or Vilnius via Minsk. Cook's Timetable, however, also shows two daily trains running only between Vilnius and Minsk, one in the morning and one in the evening, both of which are faster than the Moscow trains. I don't know how accurate the Cook's schedules are (the latest I have is from December, 2012), but it is plausible that bahn.de would omit these strictly local trains, as the responsible railway companies are not always conscientious in publishing their timetables abroad. I'm also concerned that the Lithuanian railway website doesn't show these trans. The Belarus railway website does show them though, but with one train running daily and the other thrice-weekly. Take you pick of published timetables! Reserved seats are most likely not available in advance for these local trains, so I would just wait to buy them until I got to the station in Vilnius. And although the Moscow trains can theoretically be used between Vilnius and Minsk, I wouldn't depend on the availability of a spot on short notice (these overnight trains all have seats convertible to couchettes or sleepers).