Symptoms

When trying to login to Designer, this error will be thrown:-
Authentication with server failed: logon failure: the user has not been granted the required logon type at this computer
 

Diagnoses

This is a requirement for any website hosted in IIS utilizing Forms/Windows authentication. The site users has to be granted rights from Local Security Policy in this key:-
Access this Computer From the network

This is not something specific to K2 only. The quickest way to verify this is by adding "Everyone" into that key, then trim down the scope to more specific user group.
 

Resolution

Resolved by adding the users into that Security key.