Lord Capulet introduced Paris to Juliet. He wanted her to marry this man. At the beginning he seems to advice his daughter to marry for love but then, when she does not agree to marry him, L. Capulet gets very angry. He see this as "disobedience" and so he is tough towards his daughter. He becomes aggressive and he even screams at her. This affects Juliet because he does not respect her decision and he wants to force her to accept it anyways.
I think the casket is a symbol of death and it is also a symbol of cruelty of the narrator that he took Doodle to see it and touch it to emphasize that they thought he was going to die so needed to be brought face to face with it.