Russia's upcoming Zapad drill was described as a "simulated attack" by Lithuania's government.
Poland has already agreed to purchase the system, while Sweden will be next to experience it firsthand in a joint drill with U.S.
Moscow has sent 2,500 troops to its western border region to practice landing in unfamiliar territory.
The border between Poland and Lithuania is strategically important because its seizure would cut off the Baltic states from the rest of the Western alliance.
The navy held two drills on consecutive days in the latest show of force by Putin.