If venial sin does not lead to spiritual death, then why would we pray so that “He may give him life”. Doesn’t this believer have life already since his/her sin was only venial?
Good question.

All sin, including venial sin, is abhorrent to God
1 John 3:4. However, venial sin does not cause the loss of sanctifying grace. But, venial sin is still dangerous because the more we sin venial sins, the easier it will become to sin mortal sins which do cause us the loss of spiritual life/fellowship with God.
1 Corinthians 3:16-18 We pray that those who sin venial sins will repent of these sins and serve God in the manner in which He desires to be served
Romans 12:1.
The key here is not to leave Hebrews 2:3 behind to help understand the Hebrews 6:4-6:
", if we neglect so great salvation, which was spoken unto us by those that heard the Lord and confirmed it unto us by signs and wonders and gifts of the Holy Spirit.
Hebrews 6:4-6
The Jews that Paul was writing to had saw these signs, had saw the wonders, the miracles, and also heard them from our Lord. Remember that the twelve were also sent out with the ability to do miracles raise the dead and all that. These Jews saw that, they saw the power of the Spirit, and the power of the age to come. Pauls says that if they saw, heard, and were enlightened of this demonstration of the Spirit that Jesus was the Christ and yet still didn’t believe, it were impossible to bring the Jew to repentence from their dead works.
You are correct in that Hebrews was one manuscript with no chapter and verse notations so it is important to note the context and the audience addressed.
Hebrews 2:1
Therefore we must give the more earnest heed to the things we have heard, lest we
drift away.
To “drift away” means to “lose salvation.” There are different ways to do this, but they all boil down to “disobedience” which is also called “unbelief.”
Hebrews 3:12-14
Beware,
brethren, lest there be in any of you an
evil heart of unbelief in departing from the living God; 13 but exhort one another daily, while it is called “Today,”
lest any of you be hardened through the deceitfulness of sin. 14 For we have become partakers of Christ
if we hold the beginning of our confidence steadfast to the end,
Luke 21:34-36
“
But take heed to yourselves, lest your hearts be weighed down with carousing, drunkenness, and cares of this life, and that Day come on you unexpectedly. 35 For it will come as a snare on all those who dwell on the face of the whole earth. 36
Watch therefore, and pray always that you may be counted worthy to escape all these things that will come to pass, and to stand before the Son of Man.”
John 5:14
Afterward Jesus found him in the temple, and said to him, “See, you have been made well.
Sin no more, lest a worse thing come upon you.”
1 Corinthians 9:27
But I discipline my body and bring it into subjection, lest, when I have preached to others, I myself should become disqualified.
1 Corinthians 10:12
Therefore let him who thinks he stands take heed lest he fall.
Galatians 4:11
I am afraid for you, lest I have labored for you in vain.
1 Thessalonians 3:5
For this reason, when I could no longer endure it, I sent to know your faith, lest by some means the tempter had tempted you, and our labor might be in vain.
1 Timothy 3:5-7
(for if a man does not know how to rule his own house, how will he take care of the church of God?); 6
not a novice, lest being puffed up with pride he fall into the same condemnation as the devil. 7 Moreover he must have a good testimony among those who are outside, lest he fall into reproach and the snare of the devil.
Hebrews 4:1
Therefore, since the promise of entering his rest still stands, let us be careful that none of you be found to have fallen short of it.
Hebrews 4:11
Let us therefore be diligent to enter that rest, lest anyone fall according to the same example of disobedience.
Hebrews 12:14-16
Pursue peace with all people, and holiness, without which no one will see the Lord: 15 looking carefully lest anyone fall short of the grace of God; lest any root of bitterness springing up cause trouble, and by this many become defiled; 16 lest there be any fornicator or profane person like Esau, who for one morsel of food sold his birthright.
James 5:9-11
Do not grumble against one another, brethren, lest you be condemned. Behold, the Judge is standing at the door! 10 My brethren, take the prophets, who spoke in the name of the Lord, as an example of suffering and patience. 11 Indeed we count them blessed who endure. You have heard of the perseverance of Job and seen the end intended by the Lord—that the Lord is very compassionate and merciful.
2 Peter 3:16-18
as also in all his epistles, speaking in them of these things, in which are some things hard to understand, which untaught and unstable people twist to their own destruction, as they do also the rest of the Scriptures.
17
You therefore, beloved, since you know this beforehand, beware lest you also fall from your own steadfastness, being led away with the error of the wicked; 18 but grow in the grace and knowledge of our Lord and Savior Jesus Christ.
The constant theme of the epistles is: We must remain in the grace of God through obedience to His commandments (belief in God) until we die or else we will suffer condemnation/damnation as a consequence of our disobedience/unbelief.