Failed to connect to VMware Lookup Service - https://localhost:7444/lookupservice/sdk
I found a VMware KB indicating that there could be something wrong with the SSL certificate - because I had changed the FQDN of the appliance after initial setup.
That seemed a little overkill as the appliance should work or at least you should be able to reconfigure it.
The solution was to log into the administration web interface, https://vcenter-server-name:5480, and re-run the configuration wizard with default settings. That fixed the problem and it didn't delete the cluster and folder settings that I had already configured for this given vCenter server. The vSphere web client can be reached at the following address: https://vcenter-server-name:9443/vsphere-client/#
Btw: the deafult login for the vCenter 5.1 virtual appliance is user: root and password: vmware