Baron and Countess
Lily presents herself to Monescu as a countess and Monescu to her as a baron. The irony is that both are lying to one another in order to steal from each other. But when they discover they are both thiefs they fall in love.
125,000 Francs
Madame Colet sees a purse for 3,000 francs and says that it is not worth that price. Ironically, when she sees a purse for 125,000 francs she immediately pays for it because she finds it beautiful.
Return for Reward
Monescu returns Madame Colet's purse to her in order to receive a 20,000 franc reward from her. Ironically, she is paying the man who is in fact the thief who stole her property at the opera.
Scolding
Madame Colet is a well known business woman who does the ordering around to people. When she meets Monescu he scolds her for the way she manages her money, and ironically the more he scolds her the more impressed she is with him. So much so that it leads her to give him a job as her personal secretary.
Gigolo
Lily tells Monescu that it's fine to be a crook and take Colet's money. Ironically, she tells him that to be a gigolo for her is another thing and she won't stand for that type of behavior from him.