Firstly, the English word "tempt", does not always have the meaning of "tempting to sin". Like the actual meaning of the Greek verb πειράζω, it literally means, "to test, put to the test, to try", with the hope that the person "tested", might, not will, succumb. This I believe should be the meaning used in the Lord's Prayer, "lead us not into testing", and not "temptation", which gives the false impression, that as if God does do so, and we are petitioning Him not to.
Secondly, for Jesus Christ to have been able to have sinned, He would have had to have a "fallen" human nature, which would have been "capable" of sinning. We know from Scripture, that even from the womb of Mary, Jesus Christ is called "Holy" (Luke 1:35), where the Greek ἅγιος, here has the meaning, "pure, sinless, holy". In Romans 8:3, Paul writes, "κατεκρινεν την αμαρτιαν εν τη σαρκι", that is, "He condemned sin in the flesh". The phrase depends on "κατεκρινεν". Had Paul written, "την εν τη σαρκι", then Paul would have affirmed that there was sin in the human nature of Jesus. But this construction shows beyond any doubt, that Jesus Christ, as the God-Man, even from His conception in the womb of Mary, was "sinless, pure and holy". Which is why Paul says very clearly in Philippians 2:7, of the post-Incarnate Christ, that He was "being made in the likeness of men". Here the Greek ὁμοίωμα, denotes that He "resembled" humans, not that His human nature was not real, but that, as He alone was "sinless" in His human nature, that this "separated Him from sinners" (Hebrews 7:26). This verse in Hebrews 7 is very important in the study of the Person of Jesus Christ.
"For such an high priest became us, who is holy, harmless, undefiled, separate from sinners, and made higher than the heavens"
"Holy" we have already seen. "harmless", is, ἄκακος, that is, "innocent, free from guilt". "undefiled", ἀμίαντος, "free from the stain of ungodliness, without any contamination". The great detail that is used for the Person of the Lord Jesus' human nature, is very important, lest any even suppose that in Him is ANY sin, or capability of sin.
Thirdly, The Second Person of the Godhead, the Lord Jesus Christ, from eternity past, IS Almighty God. He did NOT lay aside His Deity when He "became Man", but "took upon Himself" the "very nature" of humans, apart from any sinfulness. Jesus Christ, as His Incarnation, became the God-Man, that is, 100% God and 100% Man, both perfect natures in One Person. As "God manifested in the flesh" (1 Timothy 3:16), "God cannot be tempted with evil" (James 1:13). That is, it is not possible to "tempt God to evil", this is against His Holy Nature, they very same "nature" that IS always present in the Lord Jesus Christ. As we have seen, the human "nature" of Jesus Christ, even from conception in Mary, is completely PERFECT in every way, not only "sinless", but also "incapable of sin", by the very fact that Jesus Christ is ever the Almighty God.
Fourthly, to even suggest that Jesus Christ, the God-Man, was "capable of sinning", but chose not to, is very dangerous, and I believe something that the devil has got Christians, not only discussing, but also believing. This is nothing less than a direct attack on the very Person of the Lord Jesus Christ, with the absurd notion that somehow, a Perfect Person, can be "tempted to do evil". Exactly how this is even remotely possibe, is beyond me. Since Jesus Christ is 100% Perfect in His entire Person, HOW could He ever "given into temptation to sin"?
Christians should be very careful not to try to understand things that they are strictly not allowed to. It is like us faillible humans, trying to understand the origin of sin, where did this come from. This is a no-go doctrine for any Christian, as probing into such, wil no doubt cause you to fall into the trap of the devil.