Although I cannot answer the question on lying, (self-)speech and thinking are intimately linked to each-other, and actually used in UX-design (e.g. Krahmer, 2004). He compared two different approaches of thinking-aloud. In other words, people are perfectly able to verbalize their thoughts and actually do so.
One of the approaches he compares is a proposal of Ericsson and Simon (1993). In their nice and brief paper, they discuss (and refer to) many scientific papers (e.g. cognitive scientific and psychological) where self-speech is used during problem solving. Moreover, it showed that self-speech is related to other variables that correspond to thoughts.
In their review, Ericsson and Simon (1993) found that longer RTs were associated with verbal reports of a larger number of intermediate thoughts than those corresponding to shorter RTs. Furthermore, there seemed to be close correspondence between subjects’ thoughts and what information that they looked at--when subjects verbalized thoughts about objects in the environment they very frequently looked at them.
I must admit that self-speech in this way is only used as a methods of identifying cognitive processes, and is often a mandated task in the experiment. However, the fact that people are able to reflect on their thoughts, gives me reason to believe that they can do so unconsciously too. If someone could correct me or confirm this, I invite you to do so.