Lord Capulet's insincerity is revealed as he speaks to Paris when he states,

Death is my son-in-law, Death is my heir; 
My daughter he hath wedded. I will die 
And leave him all. Life, living, all is Death's.  (5.4.40-42)

He then states, "Uncomfortable time, why cam'st thou now /
To murder, murder our solemnity?" (lines 63-64).  Here he is basically saying that this is a bad time for him to have to deal with his daughter's death. 

Lord Capulet seems more concerned about the fact that he will not have an heir and that the timing is wrong than he actually is about the death of his daughter.  Similarly, Lady Capulet says that death has taken Juliet from her and has punished Lady Capulet.  Again, she is more concerned about her own well being than Juliet's death when she says,

But one, poor one, one poor and loving child, 
But one thing to rejoice and solace in, 
And cruel Death hath catch'd it from my sight!(4.5.49-51)

Paris too, is more worried about himself when he states,

Beguil'd divorced, wronged, spited, slain! 
Most detestable Death, by thee beguil'd, 
By cruel cruel thee quite overthrown!(4.5 58-60)