This is yet another blatant lie from a politician. THe lie is blatant, not the politician.

“This is yet another blatant politician’s lie” or "This is yet another blatant political lie”

What if I make “politician” an adjective? “A blatant politician lie”? Doesn’t it mean a blatant lie that is typically told by politicians in general?

I’ve seen many native speakers use this kind of structure. For example, I saw one man say “An educated politician’s wife” to mean “The educated wife of a politician” See? Although he put the adjective before “politician”, he used it to refer to the wife. The wife of the politician is educated, not the politician. In another example, a woman said “I gave an exasperated schoolmarm’s laugh”. Here, as in the other case, “exasparated” was referring to “laugh”, and not “schoolmarm”, even though it is right next to “schoolmarm”. Then why can’t I say “A blatant politician’s lie” to refer to a blatant lie told by a politician. This case is exatly the same as the other two. What’s wrong with it? Thank you

To answer this properly we would need more context... can you provide more of the sample that you read?