The easiest way to do LDAP authentication from a 3rd party application is to simply "bind" as the user intended.
Most applications do this by using a search, finding the valid user credentials and then binding as that specific user. Therefore the application doing the authentication needs to bind to the system first to do that search.
Note: Default install of Zimbra LDAP has an open LDAP server, this is bound to change'
See LDAP Apache as a simple example