There's another perspective on this, though, which is that it almost doesn't matter if Putin will realistically invade Lithuania. It's that we don't have a good explanation for what we would do or why, and many of the canned responses don't really logically make sense.
For instance, if Putin did invade Lithuania -- and I agree this seems implausible, but it's not unrealistic to speculate about this in the long term -- is it any more rational to defend Lithuania in that case, if the threat of nuclear weapons is real? It seems to rely on an assumption that Putin would just somehow voluntarily withhold nuclear weapons because of a legal agreement in that case, where he would not with Ukraine. Does this make rational sense given the current situation in Ukraine and the war crimes being committed?
To me this isn't theoreticals, and it's not academic. It reflects a real weakness in thinking about military policy and strategy around these points. If you believe that Russia would really use nuclear weapons in response to NATO intervention in Ukraine, there is no logical reason to assume that Russia would necessarily abstain from threatening nuclear response over intervention over Lithuania, and if the reason for abstaining in Ukraine is MAD, why would a NATO legal treaty supercede that consideration? Is it rational to uphold NATO treaties over obliteration of humankind?
My guess is Putin (or a Putin equivalent) sees use of nuclear weapons as a rational decision to the extent that he feels there's nothing left to lose. That is, if he feels he can invade Ukraine and emerge alive with Ukraine as a prize, he will threaten nuclear weapons. If he feels he can invade Lithuania and emerge alive with Lithuania as a prize, he will threaten nuclear weapons if it serves his goals. In fact, he doesn't have to have any rational justification for using nuclear weapons. He and his circle could believe that we're being invaded by space aliens and launch nuclear weapons in consequence.
Some of this becomes more absurd when you consider the tiptoeing that goes on, and the legal and logical absurdities that result. Turkey is supplying a key munition, drones, and has not been threatened by Russia at all. Why should supply of manned aircraft be different? Because they're manned? Why is all the ammo and javelins being supplied by NATO countries ok but not NATO intervention? They're clearly not the same, but some of these boundaries seem kind of imaginary or something. Is the fact that Putin is not threatening nuclear war over sanctions mean that he doesn't really feel threatened by them?
My point -- and I think Kasparov's point is along these lines -- is that a lot of the rationale NATO is giving along the lines of "we must do everything possible to avoid nuclear war" is disingenuous and fallacious. It doesn't mean we should be intervening yet necessarily, but there's something illogical about it, and it seems important to work that out in a broad sense or we're at risk for things escalating when we don't want them to.
To me, if taken seriously, the current rationale implies that any time Putin threatens nuclear weapons, we should avoid conflict. Because there's basically nothing that would be worth serious risk of worldwide annihilation. But then this leads to the position of unlimited military appeasement of dictators with nuclear weapons. Maybe that's a rational position, but it seems like we need to be clearer about where the boundaries are. My guess is if you worked it all out, you'd come to the conclusion that any nuclear military is only rational in using nuclear weapons when they are faced with existential threat themselves (that is, when they have nothing left to lose).