Just as Farfrae is the mirror image of Henchard, Lucetta is the mirror image of Elizabeth-Jane. Elizabeth-Jane is all nature and no art; Lucetta is all art and no nature. She is almost always artificial and superficial – she worries more about appearances than what is going on beneath the surface. She even defines herself in terms of her clothes; when trying to decide what dress to wear, she says:
'You are that person' (pointing to one of the [dresses]), 'or you are that totally different person' (pointing to the other) 'for the whole of the coming spring: and one of the two, you don't know which, may turn out to be very objectionable.'
It was finally decided by Miss Templeman that she would be the cherry-coloured person at all hazards. (24.6-7)
According to Lucetta, you can change your personality and become a "totally different person" as easily as changing your dress. And she certainly is changeable: she is deeply in love with Henchard when she first meets him in Jersey, but when she comes to Casterbridge, she wants to marry him only to save her reputation. When she meets Farfrae, she falls head-over-heels in love with him and forgets about her promise to Henchard.
A big key to Lucetta's character is actually her name. Her original name is French ("Lucette Le Sueur"), although she tries to disguise her French ancestry (and escape from scandal) by changing her last name to the more English-sounding "Templeman." When Elizabeth-Jane asks her if she speaks French, Lucetta blows off the question and says that "in my native isle [Jersey is an English island off the coast of France] speaking French does not go for much" (22.37). In fact, she certainly does speak French, although we're told that she "resolute[ly] avoid[s]" speaking any French at all (22.39).
Why should Lucetta be so careful to disguise her Frenchness? Well, for a long time, many English people associated French tastes and French fashions – and especially French women – with sexiness and loose morals. So it makes sense that the "other woman" in Henchard's life should be French (or at least have some French ancestry), and it also makes sense that she should try hard to look, act, and sound English when trying to escape scandal and regain her respectability and good reputation.