Lucetta is a flat character built mostly around her entirely superficial nature and her pursuit of status and wealth through just about whatever means she can think of. This single characteristic is what drives her character throughout the story.
She is also static in that she never changes her position and does not change in any way throughout the story. Though her position appears to change when she inherits a huge pile of cash, her continual worry about and concern for her status and reputation over all else comes back to haunt her.
She has married but when the letters detailing her previous affair comes out, it is her concern over her status that leads to her seizure and death.