I support all Lithuanian teams. I can't stand when people hates their own country team.
I don't care of national championships. I think it doesn't care to anybody outside the Lithuanian, so whats the difference? Course I am not from Kaunas or Vilnius either, so... I don't really matter.
Now I root against Zalgiris, but just because Z already has spot in Euroleague. 2 teams in EL is better than 1.