Back when LDS (Lightweight Directory Services) was called ADAM (Active Directory Application Mode) there was a console known as "ADAM Schema" which was the ADAM version of the "Active Directory Schema" MMC console.
Now with LDS the "ADAM Schema" no longer exists. Microsoft say to use "Active Directory Schema" for both LDS and Active Directory databases. For the TechNet article please see:
I setup an LDS instance running on TCP10001. When I try and connect to the instance using Active Directory Schema on localhost:10001 it comes up as available. However I know my instance is there as I can connect to it using ADSIEdit.
I found out if you connect using the IP address of the server's primary network interface card it connects successfully.
Must be something dodgy embedded into the code of the Active Directory Schema snap-in.