Sorry for the delay, I missed your reply.
Short answer: I don't know.
I do have some suggestions. If you are in Canad, U.S., or Australia (maybe also UK?), there are expat communities from Lithuania and Latvia. When the Soviets occupied the Baltic states, a fair number of people got out and settled in various cities around the world. There are some in non-English speaking countries, but I can't name them right now.
The Latvians tended to form stronger communities and were a bit more focused on preserving their language and culture. There was a bit more vision about eventually returning to Latvia. In large, general terms, Lithuanians weren't as focused. There are some places where there is exception and some Lithuanians did form stronger communities for cultural preservation. There are reasons for these differences, I'm skipping them.
The summary it is, do some searching for Lithuanian and Latvian cultural centers. Find any people who still speak the languages and are involved in cultural preservation. Art & music are strong in these cultures. Communicate with these folks and tell them your interests.
The two cultures & languages have some strong differences, but they are essentially sister cultures (each divided into several tribes, by the way). If you get in contact with some Latvians, they may be able (and willing) to help you track down some Lithuanians. Both peoples can get a bit "bristly" about the other, be aware of that when dealing with individuals.
Somewhere along that journey, you will find a Lithuanian cultural center of some sort, and you will be able to find someone willing and able to teach the language. Be aware that Latvian and Lithuanian are not from standard European language roots. They are considered some of the more difficult languages to learn in the world. You will also want to study Livonian, the root mother tongue which is all but extinct as a spoken language these days.