The error states the following:
"An error occurred trying to authenticate the user
More details: The server could not be contacted ------>LDAP Exception: The LDAP Server is Unavailable...."
Launch the configuration analysis to make sure that no errors or warnings are present. If you see any here, there may be a few pointing to the K2 sites needing the correct authentication settings in place.
Once this has been done you will need to make sure that the user has "log as batch job" rights which is done via the security policy settings:
Start menu > search 'Local Security Policy' > Local Policies > User Rights Assignment > Log On As Batch Job
(Right click on this and go to properties and add the domain users group or the specific account you would like to have these rights).
After this, do a repair of K2 and you should be able to access K2 Designer without any further errors.