I'm going on the assumption that you haven't visited those countries or you would realize that the sentiment runs a lot deeper than being allowed to buy NATO grade American weapons, those countries have Russian occupation in living memory and very much won't go back to those days without a fight.
> Besides, there is no reason for Putin to claim those, nor a real strategic value.
The strategic value of Lithuania or the North of Poland for Russia can not be underestimated.
> Sucks for self-determination and all that, but again, avoiding nuclear holocaust is probably worth losing the occasional battle.
It isn't the West that is threatening nuclear holocaust here, Putin did just that on live television and if that threat works this time I don't see any reason why it would not work the next.
Historically appeasement of dictators never ends well, I don't see why this would be the exception.