It is. It's very common for socially apt people to bullshit through things they don't know, or outright want to hide.
No, it’s not - you don’t even need to be literate to count symbols - but also consider the complexity of the second task and how many skills each requires: unlike counting letters, lying isn’t simple confabulation and requires a theory of mind and some kind of goal. A child who lies to avoid trouble is doing that because they have enough of a world model to know they are going to get in trouble for something even if they haven’t worked out yet that this is unlikely to work.
Pirahã language doesn't even have numerals - that's an extreme case, but there quite a few languages where people stop counting beyond certain small number and just say "a lot". Same people though don't have issues lying to one another. Let that sink in for a while - fully grown-ass adults, fully capable of functioning in their society, not capable of counting one-two-three because the concept is beyond them.
What I'm trying to say is that all of those "requires theory of mind" statements are probably true but completely irrelevant because humans (and LLMs) have "hardware acceleration" of whatever it takes to lie, meanwhile counting is an abstract idea that requires to use the brain in a way it didn't evolve to be used. Similarly, LLMs cannot count if they aren't connected to a math engine - not because they're stupid, but because counting is really difficult.