Web authentication using desktop ldap

Problem: I want users from my corporate client to authenticate with my web server by using their local LDAP credentials. Users have a local desktop client that can authenticate with the local LDAP server. My server and the LDAP server do not talk to each other.

I know it is possible to authenticate on a web server using LDAP if the web server relays the LDAP request to a LDAP server. (User/desktop client connects to web server, sends credentials and web server interacts with LDAP server for authentication)

But is there a way for a desktop client to authenticate with a local LDAP server and then connect to a web server sending a token that would grant access to the web server? (user auths with ldap, sends ldap response to webserver)

I am not talking Oauth, which requires both servers to talk. In this case, the LDAP server is isolated from outside contact.

The big problem here is that you should never trust the client, even if you have written it yourself. Something like public/private authentication would (probably) not work as well, since the problem is not the encryption, but making sure the message came as "OK" from the LDAP server. A rogue client could fake the OK and sign it anyway.