Perhaps the Amplified Bible can, uh, amplify the point we're trying to make about Jesus and Lazarus:
John 11:33-38 (AMP)
33When Jesus saw her sobbing, and the Jews who came with her [also] sobbing, He was deeply moved in spirit and troubled. [He chafed in spirit and sighed and was disturbed.] 34And He said, Where have you laid him? They said to Him, Lord, come and see.
35Jesus wept.
36The Jews said, See how [tenderly] He loved him!
37But some of them said, Could not He Who opened a blind man's eyes have prevented this man from dying?
38Now Jesus, again sighing repeatedly and deeply disquieted, approached the tomb. It was a cave (a hole in the rock), and a boulder lay against [the entrance to close] it.
The amplified Bible says that Jesus "chafed" in spirit, sighed and was disturbed! These are not the traits of a man who is empathizing.
John 11:38 (NLT)
33When Jesus saw her weeping and saw the other people wailing with her, he was moved with indignation and was deeply troubled. 34"Where have you put him?" he asked them.
They told him, "Lord, come and see." 35Then Jesus wept. 36The people who were standing nearby said, "See how much he loved him." 37But some said, "This man healed a blind man. Why couldn't he keep Lazarus from dying?"
38And again Jesus was deeply troubled. Then they came to the grave. It was a cave with a stone rolled across its entrance.
The New Living Translation says Jesus was moved with "indignation". Indignation is defined as a feeling of righteous anger. Why would Jesus be angry?
John 11:33-39 (TMSG)
33-34 When Jesus saw her sobbing and the Jews with her sobbing, a deep anger welled up within him. He said, "Where did you put him?" 34-35 "Master, come and see," they said. Now Jesus wept.
36 The Jews said, "Look how deeply he loved him."
37 Others among them said, "Well, if he loved him so much, why didn't he do something to keep him from dying? After all, he opened the eyes of a blind man."
38-39 Then Jesus, the anger again welling up within him, arrived at the tomb. It was a simple cave in the hillside with a slab of stone laid against it. Jesus said, "Remove the stone."
Here again, the Message Bible says that a deep anger was welling up within Jesus.
Go back to Strong's. If you take a look at verse 33 where it says He "groaned" in His spirit, you will see that the greek word for groan is "embrimaomai", which comes from the root "brimaomai" which means "to snort with anger". Anger! Again!
The point I'm trying to make is that this is not an illogical conclusion or a patently WoF teaching. The context very much supports the notion that Jesus was not only troubled, but indeed very upset that no one believed Him when He said this sickness will not end in death. As a matter of fact, when you consider the way that John writes it and the words he uses to describe Jesus' reaction, it becomes extremely unlikely that Jesus was simply empathizing with Mary and Martha but rather was quite upset and disgusted by the whole thing.