After hearing the news on how Lazarus is sick, John wrote about how Jesus loved Martha, Mary, and Lazarus. So Jesus went on to care for them.
But before all that, Jesus stayed for two more days in his location before heading out (11:6). At first glance, it seems to be an unconventional choice, so let's analyze it a bit. Based on the times written a few verses later, it's likely that Lazarus was already dead by the time the messengers reached Jesus. In fact, Justin Ebby noted that the delay was likely to have the total days past death be 4 days, and the Judeans thought the soul departed after 3 days (Image of Yeshua). And as we'll see later, Christ still worked -- another demonstration of Christ breaking down preconceptions with his works. Revealed Truth also had a neat explanation on the delay (as well as the rest of the story) in this post.
Once the two days are done, Jesus proclaimed that he would go to Judea again (11:7). However, the disciples had questions on why he would go there again because of how the Judeans wanted to kill Jesus. But Jesus still chooses to go because he cares for Lazarus (note that Bethany is located in Judea).
Not only that, but Jesus makes another analogy about light. He talks about how the day has 12 hours (likely referring to this specific day or a general estimated number) and that walking in the day would not lead to stumbling compared to walking in the night (11:9-10). Rather than making an absolute claim, Jesus is making an analogy where the light/day is referencing Jesus (further noted in John 1) and how we ultimately don't fall whenever we are with Jesus.
Finally, Jesus talks about how Lazarus sleeps but Jesus would wake him up. From 11:13, Jesus is referring to how Lazarus is already dead, but He still has a plan for Lazarus.