First, the passage you referenced is in Luke, not Leviticus. Second, you did not quote the correct verse. Verse 43 reads, "And He said to him, “Truly I say to you, today you shall be with Me in Paradise.” I think you meant to quote verse 46 which reads, "And Jesus, crying out with a loud voice, said, “Father, INTO YOUR HANDS I COMMIT MY SPIRIT.” Having said this, He breathed His last."
Where was the spirit of Jesus one nano second after He breathed His last? In the custody of His Father. Consider what the venerable Matthew Henry writes (see bold portion):
II. Christ’s dying explained (v. 46) by the words with which he breathed out his soul. Jesus had cried with a loud voice when he said, Why hast thou forsaken me? So we are told in Matthew and Mark, and, it should seem, it was with a loud voice that he said this too, to show his earnestness, and that all the people might take notice of it: and this he said, Father, into thy hands I commend my spirit. 1. He borrowed these words from his father David (Ps. 31:5); not that he needed to have words put into his mouth, but he chose to make use of David’s words to show that it was the Spirit of Christ that testified in the Old-Testament prophets, and that he came to fulfil the scripture. Christ died with scripture in his mouth. Thus he directs us to make use of scripture language in our addresses to God. 2. In this address to God he calls him Father. When he complained of being forsaken, he cried, Eli, Eli, My God, my God; but, to show that dreadful agony of his soul was now over, he here calls God Father. When he was giving up his life and soul for us, he did for us call God Father, that we through him might receive the adoption of sons. 3. Christ made use of these words in a sense peculiar to himself as Mediator. He was now to make his soul an offering for our sin (Isa. 53:10), to give his life a ransom for many (Mt. 20:28), by the eternal Spirit to offer himself, Heb. 9:14. He was himself both the priest and the sacrifice; our souls were forfeited, and his must go to redeem the forfeiture. The price must be paid into the hands of God, the party offended by sin; to him he had undertaken to make full satisfaction. Now by these words he offered up the sacrifice, did, as it were, lay his hand upon the head of it, and surrender it; tithēmi—”I deposit it, I pay it down into thy hands. Father, accept of my life and soul instead of the lives and souls of the sinners I die for.” The animus offerentis—the good will of the offerer, was requisite to the acceptance of the offering. Now Christ here expresses his cheerful willingness to offer himself, as he had done when it was first proposed to him (Heb. 10:9, 10), Lo, I come to do thy will, by which will we are sanctified. 4. Christ hereby signifies his dependence upon his Father for his resurrection, by the re-union of his soul and body. He commends his spirit into his Father’s hand, to be received into paradise, and returned the third day. By this it appears that our Lord Jesus, as he had a true body, so he had a reasonable soul, which existed in a state of separation from the body, and thus he was made like unto his brethren; this soul he lodged in his Father’s hand, committed it to his custody, resting in hope that it should not be left in hades, in its state of separation from the body, no, not so long as that the body might see corruption. 5. Christ has hereby left us an example, has fitted those words of David to the purpose of dying saints, and hath, as it were, sanctified them for their use. In death our great care should be about our souls, and we cannot more effectually provide for their welfare than by committing them now into the hands of God, as a Father, to be sanctified and governed by his Spirit and grace, and at death committing them into his hands to be made perfect in holiness and happiness. We must show that we are freely willing to die, that we firmly believe in another life after this, and are desirous of it, by saying, Father, into thy hands I commend my spirit.
III. Christ’s dying improved by the impressions it made upon those that attended him.
Henry, M. (1994). Matthew Henry’s commentary on the whole Bible: complete and unabridged in one volume (p. 1909). Peabody: Hendrickson.
The spirit of God cannot die. Consider that Jesus not only laid down His own life, He also took it up again. This would have been an impossibility had the spirit of Jesus died:
John 10:17-18 17 “For this reason the Father loves Me, because I lay down My life so that I may take it again. No one has taken it away from Me, but I lay it down on My own initiative. I have authority to lay it down, and I have authority to take it up again. This commandment I received from My Father.”