Russia doesn’t need justification to do anything. They can just make something up like they did in the Ukraine and Georgia. Russia shut down Estonia’s internet because they removed a statue of a WWII Russian soldier. They would clearly respond to Lithuanian involvement in Ukraine. You may not believe that Russia would invade Lithuania but they do. Lithuania recently brought back the draft to increase the size of their military and has publically protested Russian information operations in their country that they fear are a precursor to war. They would definitely not want to poke the bear.
Lithuania fears Russian propaganda is prelude to eventual invasion
I know the threat is real, but keep in mind that however hard they try to twist facts and events in their media it would not be as easy to find an even remotely believable pretext like they did with Georgia and Ukraine. Remember, in both cases Russian troops were already occupying their territories. In case of Georgia the 08 conflict was a culmination of years of provocations and 15y of cultivated war mentality, while the former Geo gov did their part with some really stupid decisions that suited their pretext just perfectly at the time. With Ukraine it was even more obvious and backstabby what happened, but again, the pretext was physical, there was chaos, and they took over without even an armed conflict because both the Ukrainian gov and military were completly disfunctional to non-existent in that period, so their pretext was, ironicaly, the threat of illigitimate action of a rogue / collapsed nation against their military assets and ethnic groups.
In case of Lithuania, if they helped out the Ukrainians in whatever capacity to fight a rebellion, it would neither be an attack on Russia nor a physical threat to it's territorial integrity and souvereignity. They can twist it as hard as they want, unless they openly acknowledge to be at war with Ukraine, nothing they might claim would physicaly and politicaly justify, not even to their public, that they've straight out attacked and invaded a foreign country. The only likely consequence I see there would be sanctions. I know I may come off incredibly naive right now and it's dead obvious that they've become far more reckless than in 2008 but even that would be a step too far for Putin. If he invaded the Baltic, that would escalate things and turn him a de-facto political corpse and Russia an official rogue nation and in war with NATO.