Structure Of Black Lives Matter Protests

Now what story have you got for us today?

Well today we're looking at the black lives matter protests that have been happening in a lot of countries around the world.

May I take it that "the black lives matter protests" is the compound noun, being the object of look at?

the black('s) protests for their lives is OK to me.

the protests for the black('s) lives is OK to me.

But this phrase, the black lives matter protests, perplexes me.

Of course, black lives matter (to somebody) is OK to me because this is a complete sentence (S+Vi).

But this LONG noun phrase "black lives matter protests" really disconcerts me. Is it common, among native speakers of English, that a sentence could be turned into a premodifier? i.e.,[[black lives matter]protests]. If so, English is super hard to learn. Honestly, I'd like to be born as a native speaker of English in the next life. I envy you to the bone.