لابس is the اسم الفاعل (active participle) of the root verb لبس
يلبس is the masculine 3rd person singular (present tense: الأفعال المضارع ) form of the root verb لبس
Five Colleges Language Video on Ism Fa2il https://www.youtube.com/watch?v=QucykPvo2ec
It's true that لابس does not literally mean "to wear" but it does mean "a wearer" as it is in the form of اسم فاعل. The sentence would then, strictly speaking, mean "He is a wearer of a hat". Of course, there's no great loss in meaning translating it as "He is wearing a hat."
You may be an Arab, but in my experience that does not say much as regards expertise in Arabic grammar. Often native Arab speakers make grave mistakes interpreting the Qur'an due to a lack of grammar.
It's quite unfortunate since Arabic is a language that once mastered allows for precise articulation of very deep ideas in speech that quite concise.