In the Garden of Eden, at the beginning of history, Adam and Eve were gven a prohibition against eating of a certain tree of the garden. They disobeyed and were thereby physically kept from eating of the Tree of Life.
To correct the ways of man, and to guide them to their ultimate salvation, God chose the people of Israel to be a light unto the nations. With the people of Israel, and with the people of Israel alone, God set up a covenant in which, fittingly, there were prohibitions on which foods could be eaten and which could not be. Anthropologically, social scientists understand how dietary restrictions are useful in helping a people define themselves as distinct, but theologically speaking, the dietary restrictions are also symbolically associated with atonement for man's original sin.
The Old Covenant of the Israelis was an aspect of God's plan to ultimately save all of mankind. Yet note that this covenant did not include provisons for mankind to partake of the fruit of the Tree of Life.
For the Christian, it is the wooden cross of the crucifixion that becomes the Tree of Life of Genesis. Jesus himself becomes the fruit of the tree. Unlike the people of the Old Covenant, banned as they were from partaking of the fruit of the tree of eternal life, in the New Covenant the dietary restrictions are lifted. Eternal life is now possible. All of mankind is invited to partake in the Food of the tree, which is the Body and Blood of Christ Himself. And when we eat of His Body and drink of His Blood, what is being offered is eternal life and eternal fulfillment.
In this way the laws of Leviticus were not abandoned, but with Christ's sacrifice, these Laws were in fact fulfilled. For Christians, the reason for the priestly laws of this book in the first place were to prepare the way for the Lord. Now all sin has been atoned for through the Christ's ultimate act of atonement. Eternity awaits.