It's a bit of a bizarre construction, especially combined with 'lunch' but I'd say that what you've been told is true:
- to be "finished" is clear-cut, you're done with the object of the sentence.
- to have "reached the end" is a little ambiguous, and while it might mean you're done, it may also imply just that you're at the end stage of the object of the sentence.
It would only work with an object that has a degree of length/complexity to it and at least some separation of stages, in my opinion. Here's an example that might be a little more idiomatic:
"I've finished the book." -- I read the whole thing.
"I've reached the end of the book." -- I might have read the whole thing, but I also might have read up to the last chapter, and not totally finished it yet.
I would lean toward the second interpretation partially because there are so many simpler ways of saying that you're finished.