The object code is the aggregate of your code and the library's header code.
If you have just your object code, you are not bound by the license of the library, then you don't need to include it.
If you have just the library header code, then you are not incorporating it into anything else, and have no obligations by the license.
If you have both the library header code incorporated into your object code , then you are bound by the license to provide attribution along with that incorporated object code.
As for you second question, I'd guess lines per file. But it is a bit ambiguous, as almost all legalese is. Again, you could just err toward caution, and include the license text regardless. Are you averse to this for some reason?
Oh, and as per the wiki link, object code is the compiled binary of your source code. At this point, whatever headers you included would already be integrated.
If that were true, why would would the FSF say that
"using the Lesser GPL permits use of the library in proprietary programs; using the ordinary GPL for a library makes it available only for free programs" [http://www.gnu.org/licenses/why-not-lgpl.html]? The LGPL is not designed to trick you into using the moral equivalent of the GPL; it's designed to occupy the middle ground between GPL and BSD licenses.
> Lesser GPL permits use of the library in proprietary programs
That means "in some cases", not "in all cases". Logical fallacy on your part.
> ordinary GPL for a library makes it available only for free programs
Here, GPL'ers contradict themselves (for both senses of "free"). GPL code can, technically, be non-gratis. And GPL code can be used in non-GPL programs (you just can't distribute them easily).
If you have just your object code, you are not bound by the license of the library, then you don't need to include it.
If you have just the library header code, then you are not incorporating it into anything else, and have no obligations by the license.
If you have both the library header code incorporated into your object code , then you are bound by the license to provide attribution along with that incorporated object code.
As for you second question, I'd guess lines per file. But it is a bit ambiguous, as almost all legalese is. Again, you could just err toward caution, and include the license text regardless. Are you averse to this for some reason?
Oh, and as per the wiki link, object code is the compiled binary of your source code. At this point, whatever headers you included would already be integrated.