This one already received an answer checkmark but here a survey of the whole passage, which explains the reasons for His grief and sadness. It was not the death of Lazarus because He promised from the very beginning that Lazarus would live, He never waivered in that. He was grieved at the lack of belief in what He had promised and the lack of belief in the person of the Son.
Everything that follows in John 11:33-44 must keep in mind what occurred in John 11:1-32. There is one common theme throughout this entire chapter--belief in the person and work of Christ. Everything Jesus does with the disciples is to bring about belief in Him and His ability to raise Lazarus from the dead. His reactions to the disciples, Mary, Martha, and the crowd are His reactions to their belief or unbelief that Jesus would raise Lazarus from the dead. Even the events following emphasize that it was about belief. In fact, John's entire gospel is about belief in Jesus--"these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name" (John 20:31).
In John 11:1-16 Jesus is informed that Lazarus is sick. The sisters having sent word that Lazarus was sick. Implicit in their sending a message is the idea that Jesus could heal Lazarus. Notice what Jesus said:
4 When Jesus heard that, he said, This sickness is not unto death, but for the glory of God, that the Son of God might be glorified thereby.
Everything that follows must keep this verse in mind--the sisters had learned from Jesus that Lazarus would live. After Lazarus died it would take a greater faith in Christ to believe that Lazarus would live but believe they should have done. So if Jesus expected them to believe His words and to believe in Him you can now easily see why later He was grieved and saddened by their unbelief.
He tells the disciples "let us go again unto Judaea again." To paraphrase their reaction -- you want to go back to Judaea? The Jews just tried to kill you back in Judaea.
..., Our friend Lazarus sleepeth; but I go, that I may awake him out of sleep.
The disciples, still fearful say, well if he's just asleep then he will be OK, we don't have to go back to Judaea where we, might die too (John 11:12).
14 Then said Jesus unto them plainly, Lazarus is dead. 15 And I am glad for your sakes that I was not there, to the intent ye may believe; nevertheless let us go unto him.
Thomas gives his reaction to the disciples and not Jesus that says OK you want to go to Judaea, OK lets go, and we can die along with Lazarus.
16 Then said Thomas, which is called Didymus, unto his fellow disciples, Let us also go, that we may die with him.
The next passage is amazing, Martha expresses her deep belief in Jesus in verses 11:17-27. There is the exchange between Jesus and Martha in which Jesus draws out her belief in Him. Jesus states affirmatively what He had said from the beginning, Lazarus would live--"Thy brother shall rise again." Martha though it would be on the last day.
Then Jesus gave a simple offer of the Gospel:
25 Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: 26 And whosoever liveth and believeth in me shall never die. Believest thou this?
Then Martha showed that to believe in Jesus is to believe things about Him.
27 She saith unto him, Yea, Lord: I believe that thou art the Christ, the Son of God, which should come into the world.
She affirms that Jesus is Lord (κύριε and not despostes), The Messiah (the Christ), and that He was the Son of God.
It's not stated exactly but I think this exchange was enough to calm the heart of Martha but it would explain why she told her sister Mary to go to see the Master.
A key to this whole passage and the questions before us is the quite different reaction of Mary in 11:32
32 Then when Mary was come where Jesus was, and saw him, she fell down at his feet, saying unto him, Lord, if thou hadst been here, my brother had not died.
OK, that is the same as Martha's initial statement. The difference is that Martha affirmed that Jesus could bring about the resurrection of Lazarus (11:22). After Mary's statement she then broke into tears, along with those who had followed.
33 When Jesus therefore saw her weeping, and the Jews also weeping which came with her, he groaned in the spirit, and was troubled.
The "therefore" applies to the first two phrases in verse 33 explicitly. Verse 35 is sandwiched between two expressions of unbelief, 11:33 and 11:36-37. So it would be reasonable to conclude that this was the reason for His grief and sadness.
God is terribly grieved and saddened whenever a sinner fails to trust in the person and work of Christ. God desires that every sinner might be saved and can you imagine how pained He would be when people fail to trust in Christ, the one and only means God has provided for sinners.
Back to the context, Mary again expressed her lack of belief in the ability of Jesus to make good on His initial promise that Lazarus would live.
39 Jesus said, Take ye away the stone. Martha, the sister of him that was dead, saith unto him, Lord, by this time he stinketh: for he hath been dead four days
Jesus, again centers everything on belief in Him:
40 Jesus saith unto her, Said I not unto thee, that, if thou wouldest believe, thou shouldest see the glory of God?
Jesus prayed to the Father, (because it is the Father that draws a sinner to the Son (John 6, Matthew 16). Notice that the Son did not ask the Father to raise Lazarus because the point was to show forth the power of the Son.
41 Then they took away the stone from the place where the dead was laid. And Jesus lifted up his eyes, and said, Father, I thank thee that thou hast heard me. 42 And I knew that thou hearest me always: but because of the people which stand by I said it, that they may believe that thou hast sent me.
Then Jesus spoke with a loud voice.
Why would Jesus have used a loud voice, When He didn't have to say even a word?
The answer to this basic question is found in the context as well, Jesus prayed to the Father in a public prayer for the benefit of those present"42 And I knew that thou hearest me always: but because of the people which stand by I said it. Jesus spoke with a loud voice so that everyone present, even over the noise of the crying, would be heard, and in being heard they would all know that it was the Son who raised Him from the dead.
43 And when he thus had spoken, he cried with a loud voice, Lazarus, come forth.
To further emphasize the most important point is belief in the Son, John doesn't mention one word about the reaction the family would have had to the raising of Lazarus. It's not that it was unimportant, it is just that what really matters in the end is how look at the Son.
45 Then many of the Jews which came to Mary, and had seen the things which Jesus did, believed on him. 46 But some of them went their ways to the Pharisees, and told them what things Jesus had done. 47 Then gathered the chief priests and the Pharisees a council, and said, What do we? for this man doeth many miracles. 48 If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation.
It comes down to either faith in Christ or a lack of faith in Christ. Faith in Christ says we believe things to be true of Him and at the same time we trust in His finished work. Not in our works but in His works, including the raising of Lazarus.