You'd first have to make a solid case that the subject in Luke 13:1 was brought up because Jesus didn't travel to Jerusalem because it "wasn't His time yet".
St. John begins by pinpointing the first Passover to
April AD 27, then his narrative continues in the order things happened. In chapter five, Jesus went again to Jerusalem to the next public festival. It would have been the ‘feast of Tabernacles’ since that was in
October AD 27, following in natural sequence from the Passover in April. Then, in chapter six the second Passover,
April AD 28, is referenced. Its context with the ‘feeding of the 5000’ anchors the middle of Jesus’ ministry to a solid date since this miracle was recorded by all four gospels.
The feast of Tabernacles comes around again in
October AD 28. As we might expect, it is the subject of chapter seven. And it seems as if Jesus remained in Judea from October until
December AD 28 because the narrative continues through to the winter festival of Hanukkah. After that, Jesus went across the Jordan River into Perea, and
“here he stayed.” Notice, he did not pass through this place but lodged and taught there, making the time
early AD 29.
During this period, Jesus heard of the death of a dear friend and said,
“Let us go back to Judea.” So, when did Lazarus die? Was it before the AD 29 year Passover or afterwards? We can't say exactly, but what we do know is that after Jesus raised Lazarus from the dead, he and his disciples left Judea again, changed house again, and resided in yet another village. By this time, Passover would have been and gone, and it would have been about
mid AD 29.
At this point, Luke provides a most interesting detail. He relates how,
“there were some present at that very time who told him about the Galileans whose blood Pilate had mingled with their sacrifices.” Galileans who could afford to do so, tried to attend the temple in Jerusalem for annual festivals. Therefore, this incident would have been either Passover or Tabernacles
AD 29, because, if it had happened in the previous year, it would have no longer been such ‘news of the day.’
So, apparently Jesus did not go to the third Passover. He didn’t go to AD 29 Tabernacles either and the reason was this: the Jews were trying to kill him, and he didn’t want to be killed ... yet. The reason he didn't want to be killed ‘yet,’ was because it was not the right ‘time.’ On one occasion Jesus had said:
“I am not going up to this feast, for my time has not yet fully come.” However, when his last year arrived, his words changed to:
“My time is at hand. I will keep the Passover at your house with my disciples.” The fourth Passover was
April AD 30