I see now why your need is not solved by Lookups or Auto-relations.
And yes, your understanding of what I was trying to say in my Test management app is right 
So at the moment, auto-relations only allow you to ask Fibery to maintain (read-only) connections that you would otherwise have to do manually, and in the specific case when you alway want to link entities based on some shared characteristic(s).
I imagine that the feature could become more sophisticated, for example employing more complex logic as the criteria for linking, and/or potentially, offering a sort of ‘default link on creation’ option, whereby the links are initially made for you by fibery, but can be manually changed/updated in the future.
If so, this could eventually be useful for your problem.
So perhaps you would have an auto-link rule that says
“On creating a Task entity:
Link to the parent Project’s Client (if there is one) OR
Link to the parent Conversation’s Client (if there is one)”
Fingers crossed that this sort of functionality is in the pipeline…