There will likely come a time that the only logical next step in your research is to contact the Archives in Vilnius. There are smaller Archives in other cities, but by and large, all surviving records have been moved from churches and municipalities to the main Archives in Vilnius. You've probably heard, and been deterred by, the three-year wait until the Archives gets to your request. This time delay is more for a multi-generational genealogical search (which I'm not even sure they do anymore) as opposed to requesting one baptism certificate, or one marriage certificate. That make take a matter of months, not years. If you have a relative in Lithuania who can order the documents for you, it may shave some time off of the process.
The other option is to hire a private researcher, a genealogist in Lithuania. Because of the time delays at the Archives and the costs, many people choose the private researcher route. If you don't have complete information--name, place, date (and who does!!???) to send to the Archives, you may not get anywhere. But that's a challenge a private researcher is paid to undertake.
In any event, the email address to contact the archives is: firstname.lastname@example.org