I am not expert on Lithuanian or linguistics As far as I know Lithuanian creators of literary Lithuanian language chose a western dialect of Aukstatijan because the region of Suvalkija & Lithuania Minor, where similar dialects were spoken
– it had some literary tradition
– it was least influenced by Slavic languages.
Modern Lithuanian has loan-words which came from the Russian language mostly according to Jūratė Laučiūtė the main source of Slavism in modern Lithuanian is the Russian language : http://www.baltistica.lt/index.php/baltistica/article/viewFile/910/837
She published a monograph (dissertation) on Baltisms in Slavic languages in 1982. The book is in Russian : https://www.dropbox.com/s/y077rpl85zephnq/%D0%9B%D0%B0%D1%87%D1%83%D1%82%D0%B5%20%D0%AE.%D0%90.%20%D0%A1%D0%BB%D0%BE%D0%B2%D0%B0%D1%80%D1%8C%20%D0%B1%D0%B0%D0%BB%D1%82%D0%B8%D0%B7%D0%BC%D0%BE%D0%B2%20%D0%B2%20%D1%81%D0%BB%D0%B0%D0%B2%D1%8F%D0%BD%D1%81%D0%BA%D0%B8%D1%85%20%D1%8F%D0%B7%D1%8B%D0%BA%D0%B0%D1%85.%201982.pdf
This articles discusses Baltisms in Belarusian language : http://www.biblioteka.vpu.lt/zmogusirzodis/PDF/svetimosioskalbos/2012/starcionok38-42.pdf
In historical context Polish and Belarusian, particularly north-western dialects of the Belarusian have a larger number of Lithuanian loan-words
partly due to linguistic shifts on Lithuanian-Belarusian border. But Slavic languages are not just Belarusian or Polish. To say Slavic languages have more Baltisms than Baltic languages have Slavic loan-words would be misleading.
Latvian and particulary the Lithuanian have retained many archaisms. But Slavic languages have also preserved many archaisms in comparison to other Europeans languages. I don’t know much about the grammar of Sanskrit, but Lithuanian & Latvian and Slavic languages have similar grammar. Both Baltic and Slavic languages have 7 cases , while Sanskrit has 8 cases. Both Slavic and Baltic languages are highly inflected languages with several declensions. So, Baltic and Slavic languages are similar in many ways with Slavic being marginally more innovative. This is from Journal of Linguistics – Case and Word Order in Lithuanian :
1.1 The puzzle
Lithuanian is a Baltic language superficially quite similar to its Slavic neighbors in terms of general properties of word order and Case. The language is basically SVO, in that this is the discourse-neutral word order, although scrambling permutations are common for familiar reasons of functional sentence perspective. Subjects of finite, agreeing verbs are typically nominative, objects of transitive verbs are typically accusative: