CRLDP Authentication : CRL lookup failed

The error you're getting is most likely not because of authentication. Do your client certificates have a CRLDP x.509 extension in them? And if so do they point to the correct URL? APM has supported HTTP-based CRLDP for a few versions now and frankly that's the better and simpler way to go if you can do it.

As for requiring authenticated LDAP, it generally doesn't make sense to do that for CRLDP (or any revocation data) resources. While it technically can be done (adding bind information to an LDAP request) via iRules and some magical VIP targeting, it isn't natively supported in the config.