> What is the equivalent in LWP::UserAgent of globoff (-g)?
There is no equivalent. LWP is not interpreting the URL in some special way like curl does so it does not need to have some way to switch this special interpretation off. Your problem must be something different.
I rather suspect that the main difference is the use of -k in curl which disables the certificate validation. While you say that you are using an insecure connection with both you don't say how you are doing this with LWP so it might be done wrong there (verify_hostname => 0 might not be sufficient). Likely the certificate returned by the server does not match the URL (i.e. the IPv6 address in it) at all and using curl without -k will likely fail too.
To get more information I recommend to run your program with SSL debugging, i.e. perl -MIO::Socket::SSL=debug4 program.pl.
