Monroe had never worked with George Cukor before and although he was in decline, he had a reputation as an excellent "woman's director." (He had directed all the great lady stars of the 30s and 40s) In "LML" there was no script to work with, and the movie was overloaded with boring "star cameos." A Marilyn was there simply to wiggle through some musical numbers and react to Montand. She has very little screen time. Cukor's directing style was languid to say the least.
He was frustrated with MM because as much as she talked about the importance of the director, she rarely seemed to react with them, preferring the advice and comfort of her drama coaches. Later, after the disaster of "Something's Got to Give" (during which he joined FOX in trying to ruin her) Cukor said: "I had very little influence on her as a director. Basically all I had to do was try to provide a comfortable atmosphere for her."
Monroe was NOT happy having Cukor direct "Something's Got To Give"--she needed a hit at that point, and she knew Cukor was not the man for the job. But, he was on her list of approved directors and FOX insisted she accept him. (The very idea that FOX put him with MM again, after he had directed Marilyn's least successful starring vehicle, pretty much proves they had very little regard for her, or cared whether the movie was a hit or not.)