John keeps speaking of the One seated on the throne as “him who sits on the throne” or with a similar phrase, never naming who it was. Moreover John also keeps describing the One sitting on the throne in a different manner, so how should we understand the difficulty John seems to be having, describing what he sees (cf. 2Corinthians 12:1-4)?
John was told by one of the twenty-four elders that the Lion of the tribe of Judah was worthy to open the book (Revelation 5:5), but when John looked up, instead of the Lion, he saw the Lamb, as though it were slain (Revelation 5:6). The Lamb was in the midst of or the middle of the throne, around which sat the twenty-four elders (Revelation 4:4; 5:6), so the Lamb was also in the midst of them. Moreover, the four beasts were also around the throne (Revelation 4:6; 5:6), and sitting in the center of it all was the Lamb. In other words the Lamb was the One on the throne (cf. Revelation 5:1).
John described the Lamb as: “…having seven horns and seven eyes, which are the seven Spirits of God sent forth into all the earth,” which, if we take into consideration the fact that seven is a complete number, means the Lamb is omnipotent or Almighty (viz. the horns being a symbol of strength), and he sees all (viz. the seven eyes). In other words, the Lamb, who is Jesus glorified, is omnipresent. The seven eyes of the Lamb or both the seven eyes and the seven horns of the Lamb (together) are the seven Spirits of God—i.e. Jesus (the Lamb who was slain) is wholly or completely God.
When considering when the Lamb (Jesus) actually received the book (Revelation 5:7), I believe Revelation 1:1-3 tells us it was already in Jesus’ possession from the very beginning, or when John began seeing this vision on the isle of Patmos. There is no evidence in chapter five that shows John is given the ability to witness something that hadn’t already occurred in heaven. Rather, he is told to write down what he had seen (Revelation chapter one), what they are (Revelation chapters two and three), and the things after those things (Revelation 4:1 to Revelation 22:21; see Revelation 1:19). Therefore, there is every reason to believe that the Lamb (Jesus) had been sitting on the throne and was already in possession of the book.
John never actually says who “sits on the throne” except to say he is God (Revelation 4:2, 9-10; 5:1, 7, 13; 6:16; 7:10, 15; 19:4). However, John does describe the One who sits on the throne. He has the appearance of the High Priest (Revelation 4:3), of a Strong Angel (Revelation 5:1-2; cf. Revelation 10:1-3) and of the Lamb that was slain, and who is Almighty and omnipresent (Revelation 5:6).
This gives rise to the question of the appearance of the One sitting on the throne. If John describes him in a certain context in one Scripture, but in another manner in a different Scripture, what does that mean? After all, it is the same Being, who sits on the throne. It is interesting, and perhaps of some importance to keep in mind, that the seraphim (the four beasts) each have a different appearance or face: a lion, a bull, a man and an eagle (Revelation 4:7). In Ezekiel, however, we are given a description of the cherubim (Ezekiel 10:15). Each one of them had four faces. They, also, had the face of a man and a lion, a bull and an eagle. However, while the seraphim had the face of either a lion, a bull, a man or an eagle, the cherubim each had all four faces. The fact that John keeps referring to God as “him who sat on the throne” and then describes him in different ways in different Scriptures (Revelation 4:3; 5:1-2, 6-7) may mean that God, Jesus in his glorified state, also has more than one face, which seems to be borne out in his creation.
In this context the Lamb “came (G2064) and took the book out of the right hand of him that sat upon the throne” (Revelation 5:7; parenthesis mine). That is, the Lamb appeared or arose (G2064) and took the book from the right side (his own right side) of him who sat upon the throne. In other words, The Lamb continually governed from the throne. It was his throne whether he was sitting or standing. The Lamb took the responsibility of disclosing what was written in the scroll at his right side.
 See Thayer’s Greek Lexicon: “1) to come: 1a) of persons 1a1) to come from one place to another, and used both of persons arriving; 1a2) to appear, make one’s appearance, come before the public; 2) metaphorically: 2a) to come into being, arise, come forth, show itself, find place or influence etc.” (emphasis mine)