Imagine, you see a non-native speaker sitting at a table with pencil and a book and notebook etc. You think he is either doing his homework or he is preparing for an exam at school.
You ask him: "What are you doing."
He says "I am studying my lessons."
This sentence sounded unnatural to me, because you would not "study your lessons" but you "learn your lesson" in English. And "learning your lesson" is more about life, rather than subjects at school.
And I thought about what might have been a better version. Maybe "I am studying a lesson/lessons." However this would not sound idiomatic either.
And finally I think "I am studying." would be enough in itself, because it intrinsically refers to school subjects.
But I still wonder, whether "I am studying a lesson/lessons" is ever used by native speakers in the sense they are doing what they were assigned at school or they are preparing for an exam at school?