To connect to the AD LDS (ADAM) instance, having local admin rights does not work. Basically, user must be a member of the "Administrators" or "Readers" AD LDS (ADAM) groups in the "Configuration" Well-known naming context.
How to add the user to the AD LDS (ADAM) groups:
1) Open ADAM ADSI Edit
2) Create a new connection by clicking "Action - Connect to..."
3) Name the connection, select the server and port in which the instance is being hosted
4) Select the "Well-Known naming context" option, choose "Configuration" from the dropdown menu and enter your credentials
5) Expand the new connection until you reach the "Roles" container (CN=Roles)
6) Double click the group you want (CN=Administrators: Full access to all AD LDS partitions, CN=Readers: Read access to all partitions) to open the attribute editor.
7) Select the "member" attribute and click edit
8) Add your accounts by clicking the "Add Windows account" button
9) Click "Ok" to submit the changes.
After this, try connecting to the AD LDS instance from the RMAD console using the account(s) specified.