'Lesson' is preferable to 'class', because 'class' suggests a group of students. If it's a one-to-one learning situation, we'd usually say 'lesson'.
In general, 'on' is the best preposition for any technology or technological media. On TV, on the radio, on the internet, on Facebook, on Skype. You could probably also say 'using Skype' or 'via Skype'.