What periods of time are implied?

Can you illustrate when “studying” takes place in each of them.

When? In all three sentences, the studying took place before the exam.
How long before the actual exam? It is unclear. We can only assume the duration of studying or the effort put in it based on the tense change in all three.

1. I studied a lot before taking this exam. It only says a lot of studying (quantity), not a lot of time before the exam.
2. I had been studying a lot before taking the exam. The ing verb in the past perfect continuous emphasizes the continuity of the action giving the impression that it was constant and quite a bit longer than #1.
3. I had studied a lot before taking this exam. It suggests that the person put more effort rather than more time in studying for the exam.

This is what I infer from those:

1) At some point before the exam, they say they did “a lot” of studying.

2) For a period that ended shortly before the exam, they say they were studying a lot.

3) Like 1), except after the exam they changed study habits in some way.

“A lot” needs to be defined.

^ A lot indicates quantity the OP is about time specifically periods of time.

Not only that, the analysis is about the sentences given as they are, not as they should be. Usually, when there is ambiguity, sentences should be rewritten with time markers, etc. But here, is about interpreting the sentences in their given tenses.

A lot can be interpreted 100 different ways by 100 different people. For 1.person “a lot” can be 30 minutes. For another it may be 3 hours.

^ a lot is a constant in all three sentences, what makes a difference is the tense used before a lot. The Q here is when…refer to the OP.