Hi E,
Thanks for taking the course and congrats on completing Lesson 1! The course structure is set up so that the homework for each lesson corresponds to what was covered in class, so yes, you definitely want to work on each week's homework after the class is done. By working on that material, along with the online resources for that lesson, you'll get an opportunity to cement the ideas from the lesson, and you'll also find that we use the homework to cover other related ideas. By going along with the course, you'll be right on pace for the October LSAT.
We generally advise against working ahead in the homeworks, but if you do want to work ahead, one thing you can do is preview the upcoming lesson, either by reading through the lesson section or by listening to the lesson concept review that Jon Denning and I do for each lesson. that's not necessary to do, but some people feel more comfortable if they have an idea beforehand of what's being covered in each lesson.
One comment about the way the lessons unfold: in the early part of the course, we really focus on introducing the core ideas of the LSAT, and so you want to worry less about doing a ton of problems and focus more on making sure you understand the basic ideas. As the lessons progress, we keep building on those ideas (which is great since if something didn't click 100% you will likely see it again later), and that's where we start to focus more on speed and practice. In other words, early on the course focus is on understanding, and then as time passes the course moves into a more practice-oriented phase in order to help you really learn to apply those ideas quickly and efficiently. As the course moves along it also adds new wrinkles to the earlier concepts and expands your total LSAT knowledge base. If anything ever doesn't make sense, just let us know and we'll do our utmost to help make it clear
Please let me know if that helps, and thanks again!