In American English, these words are used differently. Organized group instruction, at a school for example, is a class. Lessons are often individual or for small groups and usually less academic. Usually the setting alone would determine the correct word. I take piano lessons twice a week. I had my first guitar lesson this morning. I’m taking my daughter to her swimming lesson. In High School, students take 7 classes. His favorite class is math. Spanish (class) was fun today. However, you could use ‘lesson’ in a school if you want to emphasize the actual content. The teacher prepares a lesson plan. (The topics to be taught each day) Teacher: Today’s lesson will introduce the subjunctive mood.

They are synonyms, both words are correct in both sentences. Classes: a period of time in which students are taught something For example: My last class ends a four today / My classes have been cancelled and I have the day off. Lesson: a period of time in which a person is taught about a subject or how to do something. For example: My last lesson ends at four today / My lessons have been cancelled and I have the day off.

DavidK gave an excellent answer for North American English.