So, I did a bit of research on Google Ngrams and thought I'll share the details.
From my comment, I got a couple of suggestions that perfectly fits the context.
The words I suggested were:
- Taught. (Not the best option)
I searched for the occurrences of 'Completed lessons', 'Covered lessons' and 'Instructed lessons'. The result showed no occurrences for 'covered' lessons and 'instructed' lessons.
Google Ngram for 'Covered lessons', 'Completed lessons' and 'Instructed lessons'.
I further dug a bit deeper and checked for occurrences of 'Lessons completed', 'Lessons covered' and 'Lessons instructed':
Google Ngram for 'Lessons completed', 'Lessons covered' and 'Lessons instructed'.
Lessons are generally completed or covered or plainly finished (very informal).
I'll substitute one of your sample sentences with the best possible words you could use, and let you choose the best option, based on your context.
"This PHP class is responsible for retrieving data of the completed lessons from the database."
"This PHP class is responsible for retrieving data of the covered lessons from the database."
Note: For this particular sentence, I would recommend completed, as it sounds a bit better. But you should try both in your context and choose the best one.