Lets be honest, are the people running these tutoring program really in a better position than you to understand what LAT is? It is the first time LAT is being conducted. I am in my final year of Law at UNSW and I have HDed law subjects. Even then I wouldn't even be comfortable with tutoring LAT. My friends who have performed better than me and secured associateships/tip staff positions with the High Court/Supreme Court Judges are not confident either. Not sure how some people who are say in 2nd/3d year law feel that they are confident enough to run these sessions.
I guess we could help you improve your writing skills but you don't need a "LAT" tutor for that. The LAT is not a legal essay. it's just a normal essay. If you want to do well practice writing and seek feedback from your English teachers.