Sorry to be clear, HTTP::Config is not located in the /my/handler/lib directory

Yes, I understood that and it doesn't matter whether the module is there or not. You have set it up so that the process looks there first and if it doesn't have the rights to do so, that results in the fatal error message you have seen. Here's a trivial demo of this principle:

$ perl -I/root/bin -e 'use CGI'
Can't locate CGI.pm:   /root/bin/CGI.pm: Permission denied at -e line 
+1.
BEGIN failed--compilation aborted at -e line 1.
$ perl -e 'use CGI'
$
[download]

The first attempt fails because my (non-root) user has no access to the first path in @INC. The second one succeeds.