You will likely need a tool which supports an open interface that you can code an LDAP client. Most likely this is JMETER.
If you move to commercial tools many have built in integrations for LDAP testing, including LoadRunner and (I believe) SilkPerformer. It will be a balance between cost of the tool and the cost of labor. Just because the tool cost is zero (on licensing) doesn't mean the infrastructure and development costs on top will always cost less than a commercial solution with a head start. You also need to include your needs for monitoring, reporting, data analysis and what tool is easiest for your team to use and plan for.
Ask your client whether the TPS is practical and how clustered your queries need to be inside of the LDAP infrastructure. It is possible, depending upon your implementation or LDAP compliant directory service, that different branches of your LDAP infrastructure are handled by different servers