It is true that in all of us exists a measure of apprehensive awareness of death that influences our attitudes and conduct. This fear affects everyone to some degree, whether intensely or feebly, because this particular fear has a spiritual source.
Notice that verse 15 says that through the fear of death we are held in bondage all our lifetime. It does not suggest a never-ending dread, but instead a vague influence on conduct, an uncertainty wrapped within a measure of hopelessness, because we do not fully believe God-given truths about death.
God does not put people in the kind of bondage implied by this context. The author is referring to bondage to sin. We know that the source of this fear is Satan. Most of the world believes his many horrible lies regarding death: The living fear the thought of people shrieking in an ever-burning place that allows no spot of respite from fearsome pains. Some think of death as endless unawareness and others of wandering, always detached, in the vast emptiness of space.
Though humanity is certainly aware of death, it does not stop people from sinning, largely because most do not make a thoughtful, believing connection between their own sins being the direct cause of death and of Satan being their spiritual father, even as Jesus told the Jews (John 8:44). They are thus held in bondage to this deceptive, Satan-induced ignorance. As long as death seems far in the future, people generally do not pay it much attention. However, the fear still resides in their minds and influences their conduct because of not believing God's truth. So, most people do not fear to sin except for some social embarrassment because they do not make a clear, knowledgeable, believing connection between their personal sins and their own deaths.
In addition, Hebrews 2:14 tells us that Satan has the power of death. Again, people do not fear Satan very much either, and many do not even believe that he exists. Nevertheless, their ignorance does not negate the fact of their bondage. They are not aware who their slave master is, but he is a person and has a name.
Hebrews 2:14-15 and its associated verses tell us that Christ died for us to break the hold Satan had on us and any that he still has on us through fear of eternal death that might remain within us. We do not die the hopeless second death that the unconverted are still held to. We are free to turn voluntarily to God, choosing to submit in obedience to Him.
To summarize, we do not have to sin in the face of Satan's powers. We still occasionally will, but we do not have to submit to the spiritual power that Satan uses against us. The enslavement is broken. Satan is no longer our father and master.