I wonder why you tried multiple times? Did you change something between the attempts?

You have not told us which platform you are on - but most platforms offer LWP::Protocol::https from their own package management systems (and it is included in Strawberry Perl out of the box). Maybe you can avoid to go through the build cycle?

If not: The message Failed test 'have header Client-SSL-Socket-Class' might indicate that some non-Perl dependency is missing. The header files like Debian's libcrypt-dev are a likely candidate.