How can I best prepare for the essay segment of the exam?

The essay is usually either a discursive or an argumentative essay. Because of this, it is best to be prepared for both possibilities; however, the discursive essay is arguably more difficult since you have to demonstrate both sides of an argument within a short time constraint. The best way to prepare for an LNAT essay is to start writing up essays within 40 minutes, sitting down and setting yourself a timer. Past example essay questions are available online, try to answer these without conducting ANY research; you won't be able to research ahead of your actual exam either! Furthermore, the practice LNAT is downloadable, which provides you with a simulation for the essay question as well! Also helps you familiarise yourself with the interface of the exam. For passive knowledge and critical thinking skills I would recommend reading news articles to keep up to date with the world's happenings. Other than that, try to analyse common moral dilemmas. For example, chastisement of a child, higher taxation for richer people, abortion, same-sex marriage and so on. Try to create an objective view on these, think of arguments for both sides but also think about what your own opinion on the matter is. These analytical skills will carry over into your essay and you will be able to tackle the dilemma that your question addresses much quicker!