The only delivered way to use LDAP Authentication for App Designer is to use connection 3-Tier through the app server. Only with the 3-Tier connection will the Signon PeopleCode be executed. With 2-Tier, there is no hook to the LDAP Server.
You could look at using the Grey Sparling Desktop Single Signon, which does integrate with App Designer and uses Windows and NTLM to grab Active Directory authentication. This would give you some degree of LDAP Authentication if you Windows machine authenticates with a domain. But it is an add-on product you would need to purchase.
Otherwise, as Epictetus mentioned, you can use the LDAP Username if you have it synced with your PeopleSoft database and use the local password stored in PSOPRDEFN.