The LDAP service has to connect to an LDAP system. That has nothing to with LiveCycle.
I don't understand what you mean when you say that you want to connect the LDAP service to a local domain.
You can configure LC User Manager to connect to a LDAP system to retrieve a list of users. The you can query on those users. But this is different than what the LDAP service does. The LDAP service doesn't know anything about the LC User Manager. It just connects to an LDAP system directly.
When you create the users in a local domain, you're in fact creating them in the LiveCycle database. Not in a LDAP system. LiveCycle NEVER writes to an LDAP system. It only reads from it.
When LC integrates with an LDAP system (like when you create an enterprise domain in adminui), it connects to an external LDAP system and sychronizes with it. I also adds a copy of the users in its database.
The LDAP service does the same thing is the sense that it just connects to a external LDAP system to get a list of users.
If you want to query the users from the livecycle database you can use the User Lookup service (under Foundation) instead.