The four victims are Vidas Maciulevicius, Algimantas Petras Kavoliukas, Virginijus Druskis and Apolinaras Juozas Povilaitis.
"The lawsuit was filed with Vilnius City District Court on the night of January 13, the night when the USSR stormed the Lithuanian Radio and Television Centre and the Vilnius Television Tower thirty-one years ago," said Robertas Povilaitis, the latter's son, said in a statement.
The civil action was brought on behalf of six individuals who lost their loved ones on January 13, 1991.
According to the statement, the lawsuit seeks to hold Gorbachev, as the highest-ranking Soviet official, accountable for the January 13 killings.
The plaintiffs say they have submitted evidence to the court to substantiate their claim that Gorbachev, as commander-in-chief of the Soviet Armed Forces, had control of the army on January 11-13, 1991, but failed to take steps to prevent an international crime of aggression from being committed.
"It is very important that those responsible for war crimes and crimes against humanity are held accountable," said Mindaugas Gedeikis, the lawyer who helped prepare the lawsuit.
Povilaitis raised the issue of Gorbachev's responsibility in the January 13 criminal case in which the former Soviet president and commander-in-chief was not named as a defendant. Attempts were made to summon him to testify as a witness, but without success.
"I deeply regret that prosecutors from the Prosecutor General's Office did not have the courage to raise the issue of criminal liability of the then president of the USSR," Povilaitis said.
"For those who understand the hierarchical structure of the Soviet Union, it is clear that two days of action by the military forces subordinate to the USSR Defense Ministry, the Interior Ministry and the State Security Committee would not have been possible without Gorbachev's approval," he said.
"The criminal process in which some of the organizers and perpetrators of the massacre have already been convicted, is very important, but without assessing the responsibility of the top leader, justice is incomplete."
Fourteen civilians were killed and hundreds more were injured when the Soviet troops stormed the TV Tower and the Radio and Television Committee building in Vilnius in the early hours of January 13, 1991.
The Soviet Union used military force in its attempt to remove the legitimate government of Lithuania which declared independence on March 11, 1990.
In March 2019, a Vilnius court convicted 67 former Soviet officials and military officers, including former Soviet Defense Minister Dmitry Yazov, of war crimes and crimes against humanity.
The majority of them were handed prison sentences in absentia as Russia and Belarus refused to extradite them.