So His brothers said to Him, “Move on from here and go into Judea, so that Your disciples also may see Your works which You are doing. For no one does anything in secret when he himself is striving to be known publicly. If You are doing these things, show Yourself to the world.” For not even His brothers believed in Him. So Jesus *said to them, “My time is not yet here, but your time is always ready. The world cannot hate you, but it hates Me because I testify about it, that its deeds are evil. Go up to the feast yourselves; I am not going up to this feast, because My time has not yet fully arrived.”
John 7:3-8 NASB2020
Jesus was declining to travel with his brothers, who wanted him to be a showman.
Suppose a co-worker saw me leaving the office at 2:00 p.m. and asked me, “Are you going home?” and I said, “No,” but later went home that day at 5:00 p.m. Have I lied? Not at all. When I left the office at 2:00 p.m., I went to run a quick errand—I did not go home. When I departed the office at 5:00 p.m., however, I went home. “No” is often truthfully used in a time-sensitive manner. Simply because at 2:00 p.m. I said I was not going home, does not mean I could not go home at 5:00 p.m. My “no” meant “I’m not going home at the present.” Similarly, if Jesus used the term “not” [ouk] rather than “not yet” [oupo], He could just as easily been implying the same thing: “I am not going to the feast at the present.”
Context is important.
Jesus was declining to travel with his brothers, who wanted him to be a showman.
http://apologeticspress.org/apcontent.aspx?category=6&article=3781
When the proper time fully arrived, Jesus went. Yet or no yet, Jesus did not lie and your entire argument is invalid.