I think this is mostly an issue of Apache configuration and not so much about Perl:

mod_authnz_ldap completely relies on mod_ldap.

The mod_ldap example configuration shows how to set up a cache for LDAP results.

The next paragraph there discusses the (automatic...) connection pool.

I think in your mod_perl handler, you will find the user already authenticated if you set up the appropriate mod_authnz_ldap rules for the path to your mod_perl handler(s).

I now realize that you want to use the caching implemeneted in mod_ldap from your mod_perl handler. I think there should be documentation in mod_perl2 about how to call functionality exposed by other Apache modules, but I don't see anything there that would help you there...