Couple things going on here.

First, all languages have and always have had things like lenition. They're not themselves inventions. They're just labels for thing that happen naturally in language. I think you knew that, as you're hinting at the terms, not the things themselves, but it's worth bringing up for the simple fact that you having difficulty with things like lenition in a foreign language is because you're trying to learn rules for something that to native speakers would be happening without though. Just like as a native English speaker (if you are one) you didn't actually have to learn the rules of English like you are with Latin. Yeah, you were taught some stylistic trends like don't end sentences with prepositions, but these aren't actual rules. They're stylistic suggestions that change with the times. The actual things that are happening in your native language (that a foreign learner is taught rules for) are happening without your conscious thought. You're essentially learning descriptions of habits as rules.

This is important to the question you're asking, because with this in mind we can take "rules" and divide them into two types. The first type are the real rules that native speakers don't violate. For example, conjugations in unstressed positions. Not answering "Who's going with?" with "I'm" isn't something you had to be taught (or at least I didn't; one could argue that this is a change that's happening). It's the kind of rule that no one teaches because no one would mess it up in natural speech. Same for "I tomorrow go shopping will". It's not something anyone needs to teach a native speaker, so things like "use the dative" wouldn't be necessary nor meaningful.

The second type of rules, the ones which are in the minority but also are the only ones you ever hear about, are stylistic. Don't say "goin'", say "going" (of vice versa). Don't say "ain't" (except it used to be fine). Don't split infinitives (which isn't a rule except by people who were trying to make English be like Latin, which doesn't (can't) split infinitives.

Those types of "rules" are the ones you learn in grammar classes or English class or composition. They're stylistic, distinguish register rather than correctness, and well we can mostly disregard them

Now we get to the main point of the question. When were these sorts of terms used then? There are two main contexts. The first would be in the description of rules for a formalised language form. So for example if we have a liturgical version of the language that we are supposed to perceive as "pure" or classical. These are language forms which are largely not spoken in casual speech but have some other sort of religious or literary function.

The second context would be in language education texts which are older than you might think.

For the former, one of the early examples is Pāṇini, who in the 4th century BCE formulated rules for Sanskrit. They covered syntax (grammar) but also morphology (how words change within syntax). Pāṇini wasn't the first to do this, but he was the biggest in his time and has been highly regarded since.

Chinese had similarly old texts on the language itself. 2 centuries after Pāṇini, there was a text called 方言 fangyan which provided a description of regional variations in the languages of China. 方 in this context can be translated as "region" and 言 means "language". However Chinese texts were far less concerned about syntax, and when language really started getting addressed in more detail within China, it was in the context of lexicon and phonology. There isn't substantial morphological rules that needed description, so there wasn't much need to describe it in detail. It wasn't really until around the 14th century when Early Mandarin was being learned by foreigners that you'd find books like the Nogeoldae 老乞大 which explained Chinese to a foreign (Korean) readership.

The oldest European grammar I know of is Techne Grammatika (Τέχνη γραμματική), a 2nd century BCE description of Greek grammar attributed to Dionysius Thrax (Διονύσιος ὁ Θρᾷξ). Its focus was the language as used in poetry of the time, rather than explaining the basics of spoken Greek to Greek kids (because again, you don't need to do that with native speakers). Shortly after, On the Latin Language in 25 books (De lingua latina libri XXV) was produced by Varro for Latin. In it we find those similar concepts of "dative" "ablative" etc. However in it he also spends considerable time on lexicon, including etymology and derivations. In that regard it's less a grammar book like you might think, and instead should be considered simply a treatise on the language as a whole.

These are the more well known examples of what you're looking for. We can say that in general, prior to the 4th century BCE, grammar as you mean it existed, but came to Europe a bit later, and East Asia even later.