"She has a lush black hair" is at very least odd. It is grammatically well formed, in a minimal sense (subject, verb (agreeing with the subject), noun-phrase, the noun phrase composed of singular determiner, two adjectives, singular noun), but the use of countable "hair" makes the meaning very odd.
Therefore I disagree with the advice that this sentence is correct and acceptable. It does not sound natural in that context.
The countable/uncountable distinction in English is a developing process. It may, in some future version of English come to function as a type of gender, but in current English, using an uncountable noun in a countable context is merely odd.
In your particular example "a hair" would normally mean "a strand of hair". But the context doesn't allow for that interpretation. Therefore the interpretation must be that the collection of hair on her head is lush. That meaning would normally go with an uncountable noun. A native speaker may on occasion produce a sentence like this (it is grammatically English). However, An editor should remove the word "a". A native speaker may not even notice the word 'a' when reading, as the mind reforms the words in the brain.
So, this sentence is grammatically English, but it is not correct.
Similarly "it was a dirty money" is odd and does not sound natural, for the same reason.