What I was trying to ask about was the distinct characteristics of non-relative clauses and relative clauses.
Please note that you should refer to relative clauses as being restrictive or non-restrictive. Both types of clauses, restrictive and non-restrictive (or defining and non-defining) are relative or adjectival.
I liked your examples about the lions. You main question seems to revolve around this:
What I was wondering was whether 'non-relative clause' to add extra information about 'the obvious/predictable/unique/universal' features of an object.
The answer is yes (provided we understand that you refer to "non-restrictive" clauses, that is, those set off by commas). They do add extra information, and that extra information, no matter how obvious, predictable, unique or universal it may be, can actually enlighten some reader or listener who happened to ignore it.