John 11 - When Lazarus was not healed right away

1 A man named Lazarus was sick. He lived in Bethany with his sisters, Mary and Martha. ...3 So the two sisters sent a message to Jesus telling him, “Lord, your dear friend is very sick.” 4 But when Jesus heard about it he said, “Lazarus’s sickness will not end in death. No, it happened for the glory of God so that the Son of God will receive glory from this.” 5 So although Jesus loved Martha, Mary, and Lazarus, 6 he stayed where he was for the next two days. (John 11:1, 3-6, New Living Translation, 2015)

During Jesus' delay, Lazarus died. Jesus told His disciples that he was going to Bethany, to wake up Lazarus (v.11). They objected. Jesus' enemies lay in wait for Him (v.8). And, if Lazarus was sleeping, it meant he was getting better, so let him rest up (v.12). 

So he told them plainly, “Lazarus is dead. 15 And for your sakes, I’m glad I wasn’t there, for now you will really believe. Come, let’s go see him.” (verses 14-15, NLT2015)

When he arrived, Martha accused Jesus of bad timing--if He had only come sooner, Lazarus would have lived. When Jesus went to the cave where Lazarus was buried, Mary repeated the same accusation (v.32). Jesus told the people nearby to roll away the stone covering the entrance to the cave. Despite further objections from Martha that it was too late (v.39), the tomb was opened, Jesus said, "Come out," and Lazarus came back to life! 

Despite the objections and accusations, Lazarus' resurrection was an "almost ultimate healing." God was indeed glorified and "Many of the people who were [there] believed in Jesus when they saw this happen" (v.45).

Other objections could be made:

Lazarus would die again. Yet Jesus thought temporary healing worthwhile.

Miracles aren't scientific. I refer you to the short book, Miracles, by C.S. Lewis.

"Jesus wept" (v.35) at the gravesite. But if He really cared, why put Lazarus through this? Yet when Jesus said, "Come out" of the tomb, he did.. without a protest.

Despite our own questions, Jesus' own questions still stands:
25 Jesus told [Martha], “I am the resurrection and the life. Anyone who believes in me will live, even after dying. 26 Everyone who lives in me and believes in me will never ever die. Do you believe this...?” (vv.25-26, NLT2015)

Lord, We hate cancer, Alzheimer's, COPD. We hate sickness. Not only for the pain it causes. Simply put, we don't want to die. We don't want our loved ones to die. So the timing of any healing in this lifetime just isn't enough. We were made for eternal life. We long for a new heaven and a new earth.
We believe in the hope of resurrection. Dispel our unbelief. Through our risen Lord Jesus Christ, Amen.