The Gospel says Jesus loved Martha, her sister and Lazarus (11:5), and that when he heard Lazarus was sick, "he stayed two days in the place where he was" (11:6). Why did he stay?

Those two verses give no reason, and these notes don't add one. Here is what Jesus himself says, in the order the chapter gives it. When he heard, he said, "This sickness is not to death, but for the glory of God, that God’s Son may be glorified by it" (11:4). Then "after this" he said to the disciples, "Let’s go into Judea again" (11:7). And when he told them plainly, "Lazarus is dead" (11:14), he went on, "I am glad for your sakes that I was not there, so that you may believe. Nevertheless, let’s go to him" (11:15). The Gospel gives his words in that order and says nothing more about the two days.