A predicate noun is a single noun or a noun phrase that renames the subject of a sentence and follows a form of the verb "to be" or another linking verb.
A predicate noun usually have a verb that precedes it in a sentence. This verb is usually known as linking verbs. A predicate noun is usually a noun phrase.
In the given example;
"The tree by the lake is an oak"
Is serves as the linking verb.
an oak is the predicate noun because it contains a noun phrase and which renames the subject "The tree"