You can certainly say, "(the) lover of his master's wife" if you put an article in front of lover. But, you could equally say, "his master's wife('s) lover" so long as you added the second possessive in the sentence to 'wife'. There is a reason to choose the first one, what is called the 'analytic' form, over the second which we call the 'synthetic' form. The analytic form is often used to draw a person's attention to something important or easily missed. It has the added advantage of being clearer than the synthetic form because the "of the", being drawn out explicitly, shows the relationship between things. With many possessives, it may not be so immediately clear, even to a native speaker, what you mean.

Hi Monica :) How are you? I'am from turkey (İstanbul) Can we be friends?

I think "lover of his master's" is correct way to say. As for the the second option it needs the correction: his master's wife's lover But there are to many "'s" and thus it's hard to pronounce and read.

lover of his master's wife