You asked which of those three sentences makes the most sense, but I'd say it's more about context and it also depends on what you want to say.
1- I am worried about whether my student caught the gist of the lesson or not.
Here, this sentence is idiomatic and understandable to all.
You have used the preposition 'about' correctly.
2- I am worried about the understanding of the lesson by my student.
This sentence would seem to be clumsy and less idiomatic than the first sentence. Because there is the combination ing-form 'understanding' and 'by my student' (passive voice) in the sentence. I think you could re-write it as follows:
I'm worried about my student's understanding of the lesson.
3- I am worried about my student not being taught the lesson
This sentence is completely different in the meanings,
There is the use of passive gerund form (Being+past participle) in this sentence. And this sentence implies that the teacher didn't teach the students. It can also imply that the students might have attended the lesson in class but they weren't teached about the lesson. In another words, the students attended the lesson without being taught. This sentence is just like as follows:
I'm worried about my students whom the teacher didn't teach.
I'm worried (now) about my students because they weren't taught the lesson (in the past).
I think you could also say "I worry (now) about my students not being taught (now or in the future) the lesson".