I don't think it is anything about the timing. Although as you say they are similar, and might be used interchangeably, the difference is what 'lot' refers to. 'A lot of books' means many books. 'reading a lot' refers to the amount of time you have spent reading. Without 'of books', the 'lot' changes what it refers to. So - the difference is between the number of books you have read, versus the time you have spent reading them. The first would probably mean you have been reading fast. The second might suggest you have been reading often, but perhaps sporadically, so you have to keep looking back to remind yourself of where you were up to. I would also not refer to reading as a habit - the word 'habit' now has more of a negative connotation, such as a smoking habit, or a habit of picking your nose. It can also be used for things that you do for no reason, such as 'I normally just walk down that road as a matter of habit'. It would be unusual nowadays to use it for something recreational such as reading.

You are right. The two sentences are very similar. Because of the word "recently", both of those forms make sense. The slight difference would be that the second version emphasizes the activity (reading). If you want to talk about a habit, you might want to use the simple present form: " I read a lot of books." If you want to talk about a new habit, you might want to say: "I have started reading a lot of books recently."

Basically, in this context you can use either. However, there are some differences. I have read a lot of books recently. I would argue that this means the books I have read are done (I have got to the end). We are using the Pres Perfect because (a) it happened recently, and (b) I might read more. I have been reading a lot recently. I would argue that this shows the individual book is not finished (Perhaps this is why the writer of the sentence omitted the word books) Let me put these sentences another way to show the difference: I have read three books this week (They are all done, but I might read more) I have been reading the Piano Teacher by Janice Lee (I have been doing it for a while and I am still not finished) https://askpaulenglish.files.wordpress.com/2017/01/a403b-new-piktochart_548_3c73e5dc0d5647b9ed278f1d44be9953bfa5f0fc.jpeg https://askpaulenglish.files.wordpress.com/2016/05/01b20-pres2bperf2bcont.jpg