You can't know (for certain) the state of someone's mind. You can't know
that they are "pretending" rather than "wrong", only *they* know that.
If they are deliberately presenting certainty when they know they are
uncertain, you could call it lying but I think it's more a case of
unfounded confidence. It's a well known behaviour and whether you look
to Aristotle's comment "The more you know, the more you realise you
don't know" or the more modern examination of the Dunning-Kruger effect,
few would characterise it as "lying" more as not knowing enough to know
you're wrong.
To *lie* is (by definition) a deliberate act to present a falsehood as
fact. To prove a lie is hard - really hard - as it normally involves
being able to know the other's mind. If you can find a smoking gun (a
separate conversation where they admit their mind: "I really put one
over on Alan by making up those figures"), you can do it...otherwise
it's a value judgement.
So, I go back to my original response. You *can* "speak with certainty
about things about which they know they actually cannot be certain." and
not "lie". Your second version (which is different!) I still disagree
with because it requires knowledge on the other's part which
(ironically) *they* can't be certain of*.
* In most cases.
Anyway, pointless discussion so I'll end that bit.
My main point is that using inflammatory language like "you are a liar"
or "you are lying" is always likely to create more heat than light
compared with "I think you were wrong, and here's why...". Unless
someone intends to inflame the situation, such words should (IMO) be
avoided.
(What am I saying? This is on the Internet which is founded on flame
wars)