I am American, and my father's parents were from Lithuania.
I noticed recently, within the last few years, that several English Wikipedia articles were edited by someone with a Slavic background to promote the idea that Baltic languages are more related to Slavic ones than I have heard anyone claim before. I would imagine this is a controversial claim in the Baltic states.
At any rate Baltic languages are famously more conservative than Slavic ones. They are of course related as all indo-european languages are. The only question is how far back in history you have to go for that to be a relevant matter. I do not think they are close enough that it is relevant.