Well, if you recall, Cersei’s chivvying is a rather inconsistent thing – for example, she was remarkably unsuccessful at getting Ned Stark removed as Hand even after he had resigned the office.
But in that specific instance, I think A. Cersei’s unlikely to stick her neck out for Littlefinger’s man, and B. I think Robert would think that Ned has a right to pick his own men and would look unkindly at interference in this field.
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