A lucrative man’s job - modifikace “job”?

Tohle mi není zcela jasné. Vždy jsem měl za to, že přídavné jméno před genitivem modifikuje to PJ, které přivlastňuje. Je věta v názvu opravdu ok ve smyslu, že lucrative se vztahuje jen k job?

It's a question of context, and we don't have any. I would expect to see “a lucrative man's job” (if at all!) in a sentence in which the main point is that it's a job for a man, not a woman. It's clear that “lucrative” also defines “job”, not “man”, because “it's a job for a lucrative man” [“výnosný muž”]) doesn't make sense. In any case, the phrase sounds unlikely. Depending on the intended sense in the context, we'd say it in some other way.

Google: No results found for “a lucrative man's job”.

so it can be correct …and in that case the adjective modifies the whole phrase “man’s job”, I assume.

I expect so. But you have to be guided by the sense, not a rule.

• It's a sad dog's life = it's a sad life comparable to that of a dog. It's a life for a sad dog.
• It's a top-of-the-range millionaire's y­acht = it's a top-of-the-range yacht for a millionaire. It's a yacht for a top-of-the-range millionaire.
• It's a long-standing woman's prero­gative = it's a long-standing prerogative for a woman. It's a prerogative for a long-standing woman.
• it's a blue woman's dress = it's a blue dress for a woman. It's a dress for a blue woman.

Thanks. Just remembered a song where the lyrics read:.. you don’t send a boy to a dirty man’s job. Is it a dirty job? Dirty man?

Again, you could only tell from the context. I would expect this to mean that it's a dirty job, and it's for a man. It's difficult to imagine a job that could be suited mainly to a “dirty man”, a job whose main requirement is for the man to be dirty – práce pro špinavého muže??