While there is no proof of "direct orders" from Gorbachev, SSRS had made an official ultimatum for Lithuania on the 11th January. Soviets demanded Lithuania to reinstate SSRS constitution or face force. Since Lithuania did not comply with this, the events of the 13th January followed. The situation was getting more and more serious from the beginning January already. Landzbergis tried to talk with Gorbachev on the phone on the 11th, but was informed that the SSRS president is "eating".

So, even though there is no proof of direct orders, it is pretty clear that the SSRS actions during January in Lithuania were planned at the top level and OMON, together with the Red Army were following orders from " above", not acting independently.

Then again, one may challenge how much influence left had Gorbachev at the time and was it him who ordered and planned everything, or was he merely a head doing the talking while other people were making the decisions.