I'd say "I have half an hour before my lesson begins".

Correct. You could also say: "Class won't start for another thirty minutes." "I have thirty minutes free until (my) class (begins)." Class needs no article, e.g. "the", "my", "this",... Use an article for emphasis. For example, you can say "my class" to call attention to the fact that the class is yours in some sense.

Yep!