Hi there! Well, the short answer is - they were both at war with Poland and wanted their lands back (you could call this the tl;dr version). But to understand the reasoning behind it you should have the full background. In Lithuania, this period is actually known as the Lithuanian Wars of Independence.

After claiming independence in 1918, Lithuania was still a hot mess. WWI wasn't over yet German troops still occupied the country. The government wasn't really in power and there was no national army to enforce their rule. It wasn't recognized internationally by anyone until the end of the year. And in 1919 was caught between three larger forces - Soviet Russia, Poland and the Bermontians (a rogue military unit of German/anti-soviet Russians). Conflict was unavoidable, so by the end of 1918, the core of the military formed from the soldiers who came back from WWI. At the start of 1919, 3000 volunteers joined the ranks and mobilization started.

Soviet Russia, Poland and Lithuania all had wars against each other at the same time in 1919. The Soviets were trying to retake the territories that went independent during their civil war and pushed into Lithuania, taking most of the eastern region. At the same time, the Polish-Soviet war was happening in the southeast. Lithuania tried to be neutral in this conflict, but border conflicts and disputes over Vilnius and even a Polish coup against the Lithuanian government escalated into a Polish-Lithuanian war. On top of that, Bermontians started raiding the north. At one point, Lithuania had less than 1/3 of its territory from when it declared independence. After the initial soviet push was stopped with the help of German soldiers still stationed in the country and partisan efforts, Lithuanian finally had a breather and took their time to muster and train new recruits. A counter-offensive in the next six months pushed the soviets and Bermontians out.

The Soviets were also taking heavy losses from the Polish army, so a peace treaty was proposed. Soviets needed to reduce their frontline and focus on the Polish front. Since Lithuania had the upper hand, they could negotiate a better deal. Lithuanian diplomats even delayed the deals for a better strategic time, when the soviets would be more desperate because of their war with the polish army. The deal got to acknowledge Lithuania as an independent country and drew a border between both countries. Being recognized by Russia as a legitimate country led to Lithuania being recognized in the international arena by more countries. They also got Russia’s backing on the disputed Vilnius, Suwalki and Grodno regions being Lithuanian – the regions that were currently occupied by Polish forces. This led to Lithuania giving permission to Soviet forces to cross their territory, which the Russians used on their counter-attack on the Polish forces.

The peace deal ended the conflict with Russia, legitimized the country internationally and gave a chance to reclaim the rest of their territory, so working with the Soviets and keeping up on their end of the deal was in Lithuania’s interests to achieve their goals.