Designer Studio --> Org & Security --> Authentication --> Create Authentication Service
and configure WebLDAP1 with your LDAP details.
Then from the OOTB "api" package, select the Authentication Type as "Custom" and choose WebLDAP1 and save the rule. Now, all the requests to the Rule-Service-REST methods under "api " package will use Custom authentication which is LDAP in this case.
Please let me know if this works for you. I am able to authenticate successfully from POSTMAN , however I could not achieve this from my application.