Lithuania had its own Nuclear Power plant (Ignalina Nuclear Power Plant) which it closed in order to join the EU. At first, it was promising to its people that the EU will help it to build another one ("safer"), but of course nothing happened. And with the new Belorussian Nuclear Power Plant, there is no good business case for it anymore.

Further to this, one of the main concerns for Lithuania (and other Baltic states) is energy independence from Russia. Ignalina made them a net-exporter of electricity, but now almost 70% of electricity is imported, mostly from Sweden. Gas and oil mostly comes from Russia, and all national gas companies in the Baltic states are largely owned by Russian companies.

As you say there is no reason for another plant to be built in the area now, but it'll also mean the Baltic states most likely end up purchasing electricity from Belarus. As they have strong political ties with Russia, that doesn't really help their case in becoming more independent.

The same case is for Belarus. Building this station is part of becoming energy independent from buying Russian gas. Lukashenko will build it even if it's non-profitable and Lithuania won't buy energy from it. He's stubborn SOB when it comes to independence.