Note that libwww::perl is not the name of a module, there is no libwww/perl.pm - the distribution is libwww-perl. So I'm not surprised that Module::Metadata is saying that there is no module libwww::perl. It is strange, however, that ExtUtils::Installed is reporting libwww::perl but not finding LWP.pm. Its documentation says "It uses the information stored in .packlist files created during installation to provide this information", and there is a file auto/libwww/perl/.packlist - I'm not sure why it isn't looking at the contents of that file like its documentation describes, which does list LWP.pm (and I don't have too much time right now to dig into the source to see if it's some kind of bug*).
Personally, if I need a core module to check if some module is installed, I like to use check_install from Module::Load::Conditional, although that doesn't handle distribution names like libwww-perl either. You haven't said if/why you need this?
* Update: See my post here, looks like a bug to me.