I think the primary way it could escalate to war would be Lithuania rejecting the ultimatum (although I would entertain other ways of doing it).
The problem in getting Lithuania to do that would be getting them to think they would not be defeated by Poland.
The main way I could think of the Lithuanians concluding they should stand firm against the Polish ultimatum would be if Germany were whispering that it would support Lithuania (though again I could entertain other ways of it happening).
From there, we have any number of possibilities, from a Polish conquest or temporary incursion into Lithuania in a fight that is strictly bilateral, or Hitler can actually back the Lithuanians if he promised them support, thus tangling with Poland in the spring of 1938. Alternatively, Hitler could double-cross the Lithuanians and fully or partly partition their territory with the Poles. This could have interesting (and probably negative) results for Poland's international reputation.