Verse 1 begins with John saying, "I watched as the Lamb opened the first of the seven seals. Then I heard one of the four living creatures say in a voice like thunder, 'Come!' I looked, and there before me was a white horse. Its rider held a bow, and he was given a crown, and he rode out as a conqueror bent on conquest. When the Lamb opened the second seal, I heard the second living creature say, 'Come!' Then another horse came out, a fiery red one..." And so it goes on till all the horses of the Apocalypse have been described.
Then the fifth seal shows the souls of those martyred for Christ's name sake being under Heaven's altar, and so the Revelation goes on. This is all highly symbolic language, so it is not possible to be specific except to say that the Lamb in verses 1 & 3 is identified elsewhere as the resurrected Jesus Christ, who shares the throne of God in Heaven.
As verse 2 depicts one who is not the Lamb, and verse 3 states that the Lamb does something else to reveal the next rider it would be illogical to claim the rider on that white horse was the Lamb (Jesus Christ) as that logic would mean the Lamb was also the rider on the red horse, and the black horse etc. That is illogical.
So, not only does Rev. 6:2 NOT specifically mention Jesus Christ, context shows that it could not be him, given that He is called the Lamb in verses 1 & 3.