Just to echo what others have said here, the term lizard brain is a remnant of "recapitulation theory" which rigorously proposed that the embryo develops through more primitive animals. This is an intriguing idea when looking at embryos - early stage embryos of flies, birds, fish and primates really do resemble each other. So the idea was that our lower brain, near the spinal chord was the brain of a lizard, whereas the prefrontal cortex, which is highly developed in humans compared to lizards, birds etc was 'added later' and represents a 'human brain'. This idea is flawed because it basically assumed that the lizard part of us never evolved and was based on a linear idea of phylogeny, as opposed to Darwin's idea of evolutionary trees where lizards and insect continue to evolve. In evolution there are no 'lower animals'.
In practice, the parts of the brain we have in common with lizards do handle more physiologically autonomous functions (heart rate, etc). While cortex and prefrontal cortex do show greater activity in emotional and rational decision making. This is now more of a rule of thumb, not a rigorous statement or a theory of development, merely the result that structures that were developed later tend to have newer functions. A good discussion of this can be found in Gould's "Ontogeny and Philogeny".
Your question also asks why we can't rationally understand our lower brain functions...
Awareness itself is not an intrinsic property of the brain. Some aspects of the rational mind and articulate self consciousness are so far fairly unique amongst brains.
I should mention at this point that I do not mean that conscious thought is unique to humans - its clear that primates are aware that they exist and have empathy for feelings of others. Its likely that other animals have similar amazing abilities we think of as human.
Just the same, the level of development in humans is distinctly unique. Insofar as it is a unique development, not a typical brain function, we should understand that it is far from all encompassing. Given all this, its not surprising that the physiological functions of the brain such as regulation of breathing, many hormonal levels, stress are not conscious. I usually only know I've run too far and too hard because I can feel my chest heave - its actually only something I'm aware of because my brain is receiving signals from my chest that its heaving and my heart is beating rapidly.
The limits of our consciousness are the subject of much study now. From cognitive psychology and behavioral economics we've been surprised over and over in the past 20 years how there are limits to the amount of information we can process at a time and, how limited we are in being rational to the point that we can make foolish decisions, and lastly how much of those decisions are made subconciously, only to be rationalized later by our thoughts.
I will give three examples.
1) Experiments in cognitive psych show that as subjects turn over cards in a deck, our pulse and respiration indicate they know that the deck is stacked before they consciously know.
2) Psychologist/Philosopher Joshua Greene is famous for observing that moral decisions are made in parallel in more than one region of the brain before the decision is rationally made. This is a great radiolab podcast on this story.
3) Behavioral economists have shown that we don't even know a good deal when we see it. We are often convinced by cues in the environment about the profitability of our decisions which comes from pre-set processes embodied in our minds. Studies showing what happens when we pay CEOs too much money, manipulate decision making by offering too many choices and how poor people are more generous than wealthy ones.
This discussion goes back to Descartes, who felt we could be fooling ourselves to the point that we might even be deluding ourselves to believe in mathematics.
If there are ever times when people do things that don't make sense, we have often found that the faults go back to the limitations of our brains. If you have never had that experience ... "Ill have what @Sylvain's having"!
Looking at references for cognitive dissonance, optical illusions will tell you a dozen more fascinating stories. Highly recommend it :)