Given this situation (two and only two competing states), libertarianism is probably less viable. In the real world, however, you have a greater number of players.
If Libland has positive economic relations with other states (as most free people seem to prefer), it would theoretically have alternative sources of food from those allies. In addition, unless Libland's government had irrationally incited Xia's actions (theoretically, an unlikely choice for a free society), other states would see this a flagrant attack on Libland and come to its aid.
The example is certainly viable for a case where one state (out of over 200 in the real world) has a monopoly on producing any essential good, or where Xia's military is more powerful than the combined strength of all potential opposing states. I don't think the example extends beyond those corner cases, however.
My hypothesis is extreme and doesn't necessarily correspond with the real world, but proposing it and modifying it as others come up with criticisms is one pedagogical tool I would like to apply in this situation.
To answer your points:
* yes, Libland could buy Food from alternative sources. To extend the discussion I would need to adjust my hypothesis.
* no, the other states would not come to Libland's aid. If they were libertarian, they would not get involved in other states' disputes, and in any case they would know Libland would never come to their aid, so why should they reciprocate?
But the other states don't matter! If Libertarian country A is in trouble (from an aggressor, not of its own doing) and free citizens from Libertarian country B want to get involved, they are free to do so. It's none of B's government's business! It would not even occur to a Libertarian that he or she might require the government's permission.
Tho' given that the Libertarian value is long-term freedom, it's unlikely for a Libertarian nation (not the same thing as s state) to be caught napping. A Libertarian country is likely to have a well-trained and well-armed militia, but not much equipment or experience or inclination for expeditionary warfare.
If Libland has positive economic relations with other states (as most free people seem to prefer), it would theoretically have alternative sources of food from those allies. In addition, unless Libland's government had irrationally incited Xia's actions (theoretically, an unlikely choice for a free society), other states would see this a flagrant attack on Libland and come to its aid.
The example is certainly viable for a case where one state (out of over 200 in the real world) has a monopoly on producing any essential good, or where Xia's military is more powerful than the combined strength of all potential opposing states. I don't think the example extends beyond those corner cases, however.