Here's why:
* Predicate Noun: A predicate noun renames or identifies the subject of the sentence. It follows a linking verb (like "is", "are", "was", "were").
* Subject: The subject of the sentence is "The tree by the lake".
* Linking Verb: The linking verb is "is".
Therefore, "oak" renames the subject "The tree by the lake", making it the predicate noun.