Ammon cannot explain how he knew Lamoni’s mind without an explanation of who God is. Because the original Nephite text was translated into English, some of what had to have happened in this conversation is obscured. The question “believest thou that there is a God?” is understandable to modern readers, but wasn’t a question that would solicit Lamoni’s answer. The question had to have been more specific, perhaps invoking Jehovah directly, or at least a statement that there was only one God over all. It would be very unusual if King Lamoni didn’t know what gods were. He had already asked if Ammon were “more than a man,” and, therefore, he clearly had some understanding of divine beings.
Ammon’s question is about the Nephite god, Jehovah. However that was phrased, that was the intent. Lamoni does not know anything about Jehovah.