Notice Isaiah 55's symbolic terminology: thirst, waters, eat, wine, milk, bread, satisfy, listen diligently, incline your ear and come to Me, and hear and live. Within the context, all of these things imply eating spiritually.
Jesus states in John 6:51, "I am the living bread which came down from heaven. If anyone eats of this bread, he will live forever; and the bread that I shall give is My flesh, which I shall give for the life of the world." Jesus is the living Word of God. He adds in John 6:63, "It is the Spirit who gives life; the flesh profits nothing. The words that I speak to you are spirit, and they are life."
Thus, the symbolic connection is made between Isaiah 55:1-3 and "eating" of Christ. Sacrificing our lives to do this, through God's grace, leads to our making an everlasting one, to which the phrase "the sure mercies of David" alludes. The original recipients of this prophecy had already made the Old Covenant with God, but as Hebrews 8 proves, the Old Covenant was not an everlasting covenant. Thus, the covenant promised in Isaiah 55 was a future one. He is alluding to the New Covenant made with us, bringing the church directly into this context.
Understand that, even though we have made the New Covenant with God, it is not a completely "done deal" until we are in His Kingdom. This is a stern warning: Completing the agreement depends on whether we, by faith, allow Him to be sovereign over our lives.
God has greatly increased our opportunity to enter His Kingdom over what He gave to those under the Old Covenant through the gifts that He provides when we make the New Covenant with Him. These include the forgiveness of sins to justify us, access to Him in prayer, forgiveness of sin after justification, and the great gifts of His Holy Spirit—that is, His continuous grace and enabling to overcome. All are given to help us come to know Him better and be prepared.