No, He did not go straight to the tomb or to the house of Lazarus’ sisters, Mary and Martha, with whom He was known to have shared a close relationship---at least, knowledge of this close relationship is implied in the Gospel narrative. Instead, and quite curiously, Jesus is reported to have stopped outside the village. Does this not seem a bit strange? It does indeed. It does so because the one who reads the Gospel is presumably already aware of the outcome of the situation, already privy to the full story.
Because the full story is known, together with the way the story happily ends with Lazarus being raised from the dead, it is known that Jesus loved both Lazarus and his sisters. One would think that this love would compel Him to not only not delay His visit to Bethany, but also to go straight to the grieving sisters without hesitation upon reaching their town. So why does the story, as told exclusively in the Gospel of John, make the point that He did not immediately go to these people that He loved?
It may seem redundant to point out, but as the story of the raising of Lazarus begins, Jesus’ love for this family was immediately evident, as it is said that the two sisters went to the trouble of sending a message to Jesus that Lazarus was sick. Why go to the trouble to do this unless the expectation was that Jesus would come quickly to the aid of the one He loved? Coupled with Jesus’ not immediately rushing to provided the requested and likely expected assistance to His friend, this stopping outside of Bethany and not even going into the town seems doubly strange. If it seems a bit perplexing to those that would later hear or read this story, one can probably imagine that it was every bit as frustrating for these two sisters of Lazarus in that day as well, and that along with them, their fellow villagers were likely struck by the oddity of this occurrence.
Not only that, but in small, tight-knit communities as Bethany no doubt was, not only would the entire village know that Lazarus was sick, they would also know that Lazarus had died. It is likely that they would be aware of the fact that a message had been sent to the miracle-worker Jesus, informing Him of the sickness of Lazarus. They would also learn that Jesus did not respond to the message by coming to Bethany with all rapidity (perhaps even bringing a bit of shame to this family), and they would now know that when Jesus did finally make His way to Bethany, that He stayed just outside the town, forcing the grieving sisters to come out to Him.
Almost undoubtedly, they would know all of these things in the larger context of the hope of Mary and Martha that Jesus could do something about the sickness, which can be seen to be manifested in their urgent message to Jesus about Lazarus’ sickness and the words that are reported to have been spoken to Him when they finally see Him. This hope, that would eventually be vindicated by their brother’s raising at the hands and words of Jesus, would have been reasonably and understandably spurred by the healings and other miraculous occurrences that had marked Jesus’ ministry, not to mention Jesus’ love for Lazarus and his sisters.
Naturally, based on the information heretofore provided, Jesus’ visit to Bethany should be considered in the light of the parousia of the Caesar. So when one hears or reads that “when Martha heard that Jesus was coming, she went out to meet Him” (John 11:20a), a context has been created. It is here necessary to bear in mind that the readers of this Gospel, in the first century, would be quite familiar with an imperial parousia. Those that would hear this story in the world in which Jesus was said to have become King of all by His own Resurrection, would find that this going out of the village to meet Jesus, on the part of Martha, very much fits into the mold of expectations concerning an imperial visit.