How to use "have been —ing"
Solution 1:
"Have been reading" is in the present perfect continuous tense. The present perfect and present perfect continuous do not require that the action has been completed. This tense is actually used to describe actions in the past that have a connection to the present. Either the action has been completed (approximately) now or it will continue — both options are possible.
The presence of for does not change the entailments of the present perfect progressive. I could say either of the following:
- I have been reading this book for hours, and I will keep reading until bedtime.
- I have been reading this book for hours, but now I'm watching TV.
In (1), the context says that the action is continuing, while in (2), the action has stopped. The pres. perf. continuous works in both cases. The common thread is that, in both sentences, the act of reading is described with respect to the present time.
One other thing: you might notice that the present perfect construction "have read" that you have in your example is not forming a connection to the present, but rather forming a connection to a future time. This is because of something special about when clauses that refer to the future, wherein the form is present tense (in this case present perfect), but the meaning is like the future tense (in this case future perfect: "will have read").
Solution 2:
The first answer
I have been reading the book you lent me ...
just means that you are in the process of reading the book. You have begun that process and are continuing it. You have not given up, and are assuring the lender that at some point you will be able to return the book.