As one of my employees is fond of reminding me, Lithuanian has its roots in Sanscrit, and I think Latvian bears some similarities. At least, my Latvian employee and my Lithuanian employee can understand each other. It is a puzzlement how that language got from India to there!
Your employee is incorrect. Sanskrit and Lithuanian are both part of Indo-European. Sanskrit is in the Aryan (aka Indo-Iranian) branch, and Lithuanian and Latvian are in the Baltic branch.
What is true, is that Lithuanian conjugations and inflections are very close to those deduced for ancient Indo-European, as are those of Sanskrit. But there is no evidence at all that says Baltic is closer to Aryan than it is to other branches of Indo-European; in fact, it's often considered part of a Balto-Slavic family.