Ok, so on with the next part of the argument. Before anything else, I would like to say that by "will" I do not mean something which is really distinct from the soul; it is formally distinct, in that it is of the soul and not even so much as a part, but that it admits of a different definition. I'll be sloppy in my speech because it takes too long to say "the faculty through which the soul wills." Also, as far as the term "soul" is concerned, as long as anyone is at least a property dualist (admits that there are such things as mental properties) I would think the following would be fine.
First, I claim that LFW isn't inconsistent. The argument against LFW seems to be mainly that the will must be either determined or random ("indeterministic" as it is usually put, though I shall reserve that word for other purposes); since LFW isn't determined, it must be random.* I hold that it is neither, that this is a false dichotomy. They may certainly describe acts of the will: we can tally up acts of the will already completed and say that in circumstances C, agent X has done Y and so have descriptive determinism, or we can say that agent X has n choices and will choose one out of those n and so have descriptive randomness (or maybe even other degrees of probability). This doesn't actually explain how the will works, however, and need not be damaging to the LFW enthusiast.
As for how the will works, it is either completely caused, or not completely caused. This is different from the usual dichotomy, which is that it is either completely caused or completely uncaused. I maintain that there is a space in between the two, and so that denial of both explanatory determinism and explanatory randomness is not incoherent. Further, I claim that the supporter of LFW is not thereby obligated to explain what this middle ground is, as she cannot explain it. This inability to explain how LFW works is supported on rational grounds and so is not mystery for mystery's sake.
It is clear from experience that there are things which cannot be understood completely rationally without any need to get mystical. A person cannot even understand what red is simply in terms of ratiocination. However, in that case we can explain that red is a color and has differing degrees of similarity to purple, orange, yellow, blue, and so on. When it comes to LFW, we do not have that luxury. We can say how it is different from everything else, but we can only supply to barest elements of similarity. Because natural (deterministic) things have a potency to a given action in a given situation, we can analogize with that and say that the will has a potency for opposite actions in a given circumstance.** Other than this, there is nothing similar in kind to the will. Its defining characteristic is a completely qualitative difference from that which is natural, and there really isn't anything which doesn't fall into one or the other camp (either it has a potency for opposites and is volitional, or it doesn't and it is natural). Therefore, we cannot explain the key feature of the will in terms of similar things.
Further, we cannot explain the properties of the will in terms of cause and effect. Going by the nature of the will, we can merely tell that it has a potency for opposites and not what it will actually choose, or how. Going by the effects of the will, we can only know what it has actually caused. Alternatively, we could analyze the cause of the will. Theistically, this is ultimately another will and so the contingent acting of the will is a brute fact of the world, as God's will cannot be further explained by another cause. The contingency in God's will is furthermore responsible for the contingency in our wills.
Of course, I haven't really proven that the will's workings cannot be rationally understood, but I consider the preceding to be good indications which place the ball in the anti-LFWers court. Next time, I hope to start building up something positive to say about how the will works. Given the above, there will always be a point in each illustration where we cannot intellectually understand how things work, but I think that other features in each situation are reasons for accepting LFW nonetheless.
* - I know that there's more out there; I simply haven't researched it enough to talk about it here. Feel free to chime in if you have something to add.
** - Along these lines, Scotus reinterprets Aristotle's notion both of potency to opposites and the notion of a rational faculty which has such a potency, so if you are wondering why this doesn't jive with the Metaphysics, blame Scotus. In short, Scotus uses a synchronic and logical/metaphysical notion of possibility to undergird the potency for opposites, while most earlier philosophy uses a diachronic and statistical notion.