WHAT THE HELL HAS HAPPENED TO LWP IN PERL 5.6.1?
Nothing. LWP is not distributed with Perl and never has been.
You have probably configured
Perl 5.6.1 to look for modules in a different
place than 5.6.0 was, so it doesn't see that copy of
that you installed before.
Either reconfigure 5.6.1 to look in the right place,
or copy all the locally-installed modules from the
old library directory to the new one. The
autobundle feature in the CPAN
module might be useful if you need to copy the modules.