What is Lauren's Fallacy?

This is a red herring in that it answers the question, "Can you legislate away evil?".

A more pertinent question is, "Can legislation diminish the probability that evil intentions will lead to suffering?"

I would be far more interested in her answer to this question.

Whether something is a red herring depends upon the subject under discussion. The red herring fallacy is a deliberate diversion of attention to abandon the original argument. From the amount of information you provide here, one must guess exactly what the underlying subject is. As a naked statement, "You cannot legislate away evil" might be the proposition under discussion, in which case the concept of evil and how to deal with it is not a diversion but the focus. 

I think a better argument can be made for a strawman fallacy . Remember this: arguing over fallacies is often a red herring itself. If there is clearly a reasoning error, one person might assign a named fallacy that may or may not be a good match, and the argument will shift to debating if that fallacy matches or not rather than focusing on the problems with the statement in the first place. This is why I prefer to use the "safest" fallacy that takes very little argument to support.

As far as I am aware, nobody is suggesting that we should "legislate away evil" or that such a thing is even possible. Offering a charitable interpretation of this comment, she is likely suggesting that stricter gun laws won't result in a decrease in mass shootings. Had she said what she meant rather than attempting to offer an emotional soundbite, a more productive and evidence-based discussion could be had on the merits of that claim.

It's downright hypocritical when you consider the legislating body, the Supreme Court, and the effort of zealous Christian fanatics in political office are indeed engaged in legislating morality. 

So the statement is clearly a deception and a distraction. I can certainly see the case for a red herring fallacy, but begging the question and non sequitur are likely contenders as well. 

Evil is a religious moral concept. The legislature is empowered to create laws for regulating society for the common weal. The claim assumes the function of government is not in the business of legislating morality, but, in fact, the claimant's political rhetoric and claim to fame are doing exactly that.