Poison him.
Lady Capulet does not want to kill Romeo. She is Juliet's mother and does not harbor any intent to harm Romeo in the story of Romeo and Juliet.
On the Capulet side, Tybalt, Lady Capulet, and Paris died. Tybalt was killed by Romeo, Lady Capulet died of grief, and Paris was killed by Romeo in a duel.
Tybalt is associated with the Capulets, and he thinks of himself as a Capulet, but he is actually not a Capulet at all. He is the son of Lady Capulet's brother, and Lady Capulet is only a Capulet by marriage. That is why it is Lady Capulet, and not Lord Capulet, who is so furious with Romeo after he kills Tybalt.
They are only referred to as Capulet and Lady Capulet.
Your question is unclear. Is Duty a different play from Romeo and Juliet which also has a character called Lady Capulet? (actually, the character in Romeo and Juliet was not called Lady Capulet in Shakespeare's time--since Capulet was no lord, she could not be a lady. She is called the much simpler "Mother".)
Benvolio convinced Romeo to go to the Capulet's party.
In William Shakespeare's play "Romeo and Juliet," Lady Capulet is known only by her title as "Lady Capulet." She is referred to as Juliet's mother throughout the play and her first name is not disclosed.
Juliet says that she will not be satisfied until Romeo is dead, and she wants to mix the poison that her mother will send him.
Lady Capulet.
Lady Capulet supports Juliet's marriage o Paris.
Romeo, Juliet, Lord Capulet, Lady Capulet, Friar Lawerence, Nurse, Tybalt, Mercutio, Benvolio
Romeo Juliet Lord Capulet & Lady Capulet Lord Montague & Lady Montague Mercutio Benvolio Tybalt Paris Friar Lawrence Nurse The Prince