I've heard terms like grammatical category and grammatical feature being used for inflectional properties such as number, person, tense, mood, and so on. Gender is commonly included in this list too, but I see a distinct difference with it. Gender describes the lexeme, while the others describe inflections.
Is there an established term for what I'm calling lexeme-describing grammatical features? Is noun class the term I'm looking for? Does this term really cover all bases, as it refers specifically to nouns? If you take all languages into account, don't you find examples of lexeme-describing grammatical features that describe other words than nouns?