Are the Live Lessons recorded?
Only if you want them to be. You can manage your privacy settings here: privacy settings.
If you opt in, you will be able to go back and see replays of all of your old lessons on your Achievements page. The records include video, audio, chat messages, and exercise information for each lesson.
As a student, the recordings can be very useful to see your progress, and to jog your memory of tips from your tutors.