I would have to say screw her and drop it. It's her fault and the department's fault for not issuing times sooner, or perhaps she could have drummed up more interest in the class.
You have to take into consideration that the lsat is perhaps one of the most important tests you'll take in your career, since you've decided to go to law school. You should just explain to the woman that this is your situtation, and you're really very sorry, but due to the importance of this test, you can't jeopardize your score for the sole reason of the class being cancelled. Despite the fact that it's a small department, the costs of stressing yourself out and hurting your score, are, in my opinion, greater than whatever minor effect this woman may have on your reputation. If it's such a small department, other professors should have had their own dealings with you, and will have made their own opinion of you. It shouldn't change much just because this woman has an issue.