This is a very difficult question to answer. There's some crossdisciplinary work that combines sociolinguistics and social networking, and it suggests that linguistic innovations tend to come from peripheral members of a group, and tend to happen less often in smaller groups. The reason they come from peripheral members of a group is that these are the people who are engaged in many different groups, and so are exposed to more variation. The reason smaller groups tend to be less innovative is that in smaller groups it's much easier for every member to have a strong connection to every other member. Milroy and Milroy 1983 is a good place to start.

So, there are some general reasons why some communities are more or less innovative, but what about Lithuanian speakers in particular? It's not that they weren't exposed to other languages: all the evidence points to very close contact between Baltic and Slavic speakers until the modern day. Part of the reason for the conservatism of Baltic has to do with the fact that Balto-Slavic and Late Proto-Indo-European are practically synonymous constructs. Balto-Slavic didn't really 'split' from PIE so much as the ancestors of all the other groups left the Ukrainian and Russian steppes and the linguistic ancestors of Balto-Slavic speakers are all who were left. This gives Balto-Slavic something of a head-start on Germanic, Italic, Celtic, etc.

Finally, I feel compelled to point out that while Lithuanian is quite conservative (at times it looks practically like Proto-Balto-Slavic) it nonetheless has several innovations of its own. Its pitch-accent system is all messed up from the PBS system, it's lost the neuter in its nominal system. It has a larger vowel system than PBS, it's lost its nasal vowels (themselves innovations!), and its mixed up historic *a and *o.