The Debian (and Ubuntu) package for a distribution Foo-Bar is always named libfoo-bar-perl.
For most modules like WWW::Mechanize the distribution has the same name as the main module, so look for a package libwww-mechanize-perl. I Don't know if there is such a package in your distribution.
(LWP is a bit special in this regard because the distribution predates the package names that we now know. Luckily apt-cache search perl lwp turns up libwww-perl - WWW client/server library for Perl (aka LWP).)