'Lay' requires a direct object but 'lie' does not..
Lay is transitive and Lie is intransitive.
'I lay the book down on the table' (the book is the direct object)
'I lie down' (there is no direct object here, just a subject/nominative 'I'
In the DL sentence the clause is 'a spoon lies' because the spoon is the subject of the clause and not a direct object.
This seems to be a confusion of transitive and intransitive verbs.
You can lie somewhere with no object (intransitive) or you can I inflict lying on something, the object (transitive). The verb then would be to put or to lay.
You don’t have to lay the object itself. You can also lay a table by putting other things on it. Or be abstract and lay out a plan.
A similar distinction exists in German.
to lie - liegen
to lay - legen
In the example the spoon is the subject. It does not put/lay itself somewhere it simply lies (intransitive).