Was Jesus The Lamb of God or the High Priest (that offers the lamb as a sacriffice)?

For the start of the answer, lets look at

Colossians 2:16-17 New King James Version (NKJV) 16 So let no one judge you in food or in drink, or regarding a festival or a new moon or sabbaths, 17 which are a shadow of things to come, but the substance is of Christ.

Jesus is the true fulfillment of the things in the old testament which are "shadows" or representatives, pointing to the true thing to come.

think of the Sabbath

Hebrews 4:9-11 There remains therefore a rest for the people of God. 10 For he who has entered His rest has himself also ceased from his works as God did from His.

Compare with Christ statement in Matthew 11:28-30

28 Come to Me, all you who labor and are heavy laden, and I will give you rest. 29 Take My yoke upon you and learn from Me, for I am gentle and lowly in heart, and you will find rest for your souls. 30 For My yoke is easy and My burden is light.”

Jesus is more things also, look at the "I Am" statements in John's gospel.

Then Jesus declared, “I am the bread of life. He who comes to me will never go hungry, and he who believes in me will never be thirsty. (John 6:35)

When Jesus spoke again to the people, he said, “I am the light of the world. Whoever follows me will never walk in darkness, but will have the light of life.” (John 8:12)

I am the gate; whoever enters through me will be saved. He will come in and go out and find pasture. (John 10:9)

“I am the good shepherd. The good shepherd lays down his life for the sheep.” (John 10:11)

Jesus said to her, “I am the resurrection and the life. He who believes in me will live, even though he dies; and whoever lives and believes in me will never die.” (John 11:25-26)

Jesus answered, “I am the way and the truth and the life. No one comes to the Father except through me.” (John 14:6)

“I am the vine; you are the branches. If a man remains in me and I in him, he will bear much fruit; apart from me you can do nothing.” (John 15:5)

One simply cannot over-state how important Jesus Christ is. The Bible is about him.

Colossians 1:15-17 He is the image of the invisible God, the firstborn over all creation. 16 For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him. 17 And He is before all things, and in Him all things consist

There is no need for an "either, or" question here, for Jesus is both! Throughout the Bible Jesus is constantly given a variety of names, titles and roles. Consider Isaiah 9:6 with this list: "And his name shall be called Wonderful, Counsellor, The mighty God, The Everlasting Father, The Prince of Peace."

It is the same with the functions he performs. In addition to those ones above (Counsellor and Prince) he is also called the Mediator, the Great High Priest, the Judge of all the earth, the Shepherd of the sheep, the Gate, and so on.

Hebrews 9:11-12 combines two of the functions Jesus carried out, which are not mutually exclusive for God incarnate. They would have been had Jesus not been fully human and fully God, but because he added human nature to his divine nature, he can simultaneously be a sin offering AND the great High Priest who presents his own blood as the only perfect offering for sin there has ever been. Thus these verses say of the resurrected Christ, "But Christ having being come an high priest of good things to come, by a greater and more perfect tabernacle, not made with hands, that is to say, not of this building; Neither by the blood of goats and calves, but by his own blood he entered in once into the holy place, having obtained eternal redemption." This High Priest used his own shed blood to enter into heaven, not the blood of mere animals that can never take sin away.

It is the same when we read of Christ in heaven, sharing the throne of God. Revelation 3:21 has Jesus saying that he overcame "and am sat down with my Father in his throne". Chapter 5 describes one called the Lion of the tribe of Judah, who is also standing in the midst of the throne as a Lamb that had been slain. Jesus is both a Lion and a Lamb. Chapter 22 twice speaks of "the throne of God and of the Lamb" - one throne. Jesus both sits on that throne and stands in the middle of it. Language is being used to convey to us earth-bound humans something beyond our ken. Things in heaven are so utterly 'other', we have to enter into the literary devices used by the writers who, under inspiration of the Holy Spirit, described the indescribable.

He was both, but offered Himself, His own body as the perfect sacrifice. The book of Hebrews goes into great details. If you have a little time, read an overview commentary of Hebrews; if you have a medium amount of time, read a study Bible or commentary that goes verse by verse; If you have a lot of time, I strongly recommend the Naked Bible podcast by Dr. Michael Heiser, wherein he breaks down the book in great detail using a lot of knowledge of 1st Century Middle Eastern cultural background, but explains things in laymen's terms. He covers the book of Hebrews over several episodes. If you wish, you could focus on Hebrews 10, which deals specifically with the sacrifice.

Starting from verse 4 (I'm using the NLT): "4 For it is not possible for the blood of bulls and goats to take away sins. 5 That is why, when Christ came into the world, he said to God,

“You did not want animal sacrifices or sin offerings. But you have given me a body to offer. 6 You were not pleased with burnt offerings or other offerings for sin. 7 Then I said, ‘Look, I have come to do your will, O God— as is written about me in the Scriptures.’”

8 First, Christ said, “You did not want animal sacrifices or sin offerings or burnt offerings or other offerings for sin, nor were you pleased with them” (though they are required by the law of Moses). 9 Then he said, “Look, I have come to do your will.” He cancels the first covenant in order to put the second into effect. 10 For God’s will was for us to be made holy by the sacrifice of the body of Jesus Christ, once for all time.

11 Under the old covenant, the priest stands and ministers before the altar day after day, offering the same sacrifices again and again, which can never take away sins. 12 But our High Priest offered himself to God as a single sacrifice for sins, good for all time. Then he sat down in the place of honor at God’s right hand. 13 There he waits until his enemies are humbled and made a footstool under his feet. 14 For by that one offering he forever made perfect those who are being made holy.