I'm going to shift from science-based to science-fiction. This will make sense as you read the answer.
Lying is a choice
Current thinking about the psychological processes involved in deception holds that people typically tell the truth more easily than they tell a lie and that lying requires far more cognitive resources. First, we must become aware of the truth; then we have to invent a plausible scenario that is consistent and does not contradict the observable facts. At the same time, we must suppress the truth so that we do not spill the beans—that is, we must engage in response inhibition. What is more, we must be able to assess accurately the reactions of the listener so that, if necessary, we can deftly produce adaptations to our original story line. And there is the ethical dimension, whereby we have to make a conscious decision to transgress a social norm. All this deciding and self-control implies that lying is managed by the prefrontal cortex—the region at the front of the brain responsible for executive control, which includes such processes as planning and regulating emotions and behavior. (The Art of Lying)
That paragraph tells us some useful things:
We don't actually know what part of the brain encompasses "lying." This will make more sense momentarily.
The part of the brain that might control lying is the prefrontal cortex.
- Lying appears to require more cognitive resources. In other words, we need to think about lying while we don't need to think about the truth. Why?
We must know there is a truth before we can invent a lie. That's important. Theoretically, a "truth serum" would have no effect on someone who believes they know the truth.
A lie must be invented. It may be a preconditioned response (i.e., "practiced"), but it must nevertheless be constructed after the truth is known.
Finally, when a lie is told, the truth is suppressed. We can assume a practiced liar is someone who's good at suppressing the truth, but I can't find any science to back that idea up. In other words, it's like lifting a 4kg weight. We can practice to the point that it's "easy" to lift the weight, but we must lift the weight, nonetheless, and we know we're lifting it regardless the ease.
But the choice requires a reference
Beliefs are not just cold mental premises, but are ‘hot stuff’ intertwined with emotions (conscious or unconscious). Perhaps, that is why we feel threatened or react with sometimes uncalled for aggression, when we believe our beliefs are being challenged! Research findings have repeatedly pointed out that the emotional brain is no longer confined to the classical locales of the hippocampus, amygdala and hypothalamus. The sensory inputs we receive from the environment undergo a filtering process as they travel across one or more synapses, ultimately reaching the area of higher processing, like the frontal lobes. There, the sensory information enters our conscious awareness. What portion of this sensory information enters is determined by our beliefs. Fortunately for us, receptors on the cell membranes are flexible, which can alter in sensitivity and conformation. In other words, even when we feel stuck ‘emotionally’, there is always a biochemical potential for change and possible growth. When we choose to change our thoughts (bursts of neurochemicals!), we become open and receptive to other pieces of sensory information hitherto blocked by our beliefs! When we change our thinking, we change our beliefs. When we change our beliefs, we change our behavior. ... Total brain function is required in stabilizing the belief and in responding to environmental system. Some of the brain regions and the neural circuits are very important in establishing beliefs and executing emotions. Frontal lobes play a major role in beliefs. Mental representations of the world are integrated with sub-cortical information by prefrontal cortex. Amygdala and Hippocampus are involved in the process of thinking and thus help in execution of beliefs. NMDA receptor is involved in thinking and in the development of beliefs. (The biochemistry of belief)
There isn't a specific part of the brain that regulates "lying." There are parts of the brain that are involved with the choice to lie. As previously mentioned, the ability to lie begins with knowledge of the truth — but what, really, is truth? It's one thing to stick our finger into a light socket and thereby learn the "truth" about electricity. It's another to be told the location of a pot of gold... and believe it's the truth.
So, while the prefrontal cortex could be used to simplistically rationalize a chemically-induced inhibition to lie, a more complex solution is a chemically-induced change to the frontal lobe that strengthens beliefs. The stronger the belief, the harder it is to lie about it because denial of the belief is emotionally connected (and this is my opinion) to your personal sense of self-worth.
But it could also be said that, since many aspects of the brain serve to filter incoming sensory data through our systems of belief, that the chemical reduces the strength of those filters, resulting in a higher likelihood that what is said is "the unvarnished truth" (as the police would say, "an excited utterance") and not a fabrication, consciously or unconsciously. However, since this isn't addressing just one aspect of the brain, the onus would be on you to explain the more complex consequence of the drug since the affected area of the brain is no longer carrying a significant burden toward suspension of disbelief.
But there's a third choice...
Finally, we could attack the area of our brain that governs, somewhat generally, that we care about things. The amydgala is an area of your brain responsible for emotional processing, especially fear and anxiety. When you really, really, really simplify things, we lie because we're afraid or anxious. We want a better deal than we deserve, or we don't want to get caught, or we're passionate about keeping a secret... If your chemical stunts the effects of the amygdala, then what you've removed is the subjects ability to care about keeping the secret.
Because lying is a choice and not an autonomic response of the body, it is unlikely that there is just one part of the brain that governs lying. In a complex story explanation, your "truth serum" could (and likely would) be a concoction of chemicals that affect different parts of the brain in different ways. One that inhibits the subject's ability to think about altering the truth; another that strengthens the value of the truth to the subject, making it harder to lie about without causing emotional turmoil, and a third that interferes with that emotional control to reduce the subject's ability to care about the truth as something valuable at all.
Or any other combination of effects. Lowering inhibition, increasing anxiety (the "excited utterance"). Perhaps my main point is that lying is a complex behavior and a suitable world explanation would require an equally complex series of effects that would rationalize the idea of "I can't lie about it" to the reader.
Can you see why I asked if I could answer as science-fiction? We really don't know what, specifically, the brain does to affect a lie. We can measure what parts of the brain light up when someone does lie, but we really don't have a clue about how humans do it. That's why I had to step away from science-based.