Someone's Probably Lying, Right?

Relevant wiki: Truth-Tellers and Liars

* The wording of this question has been changed since I posted my solution. For reference, "knaves" are the liars and "knights" are the truth-tellers. *

We will look at the $4$ options that can be assigned to the "lying down" inhabitant, (#1), and see how these options play out with regards to the other two inhabitants. These $4$ options are generated by whether or not #1 is a knight or a knave, and by whether of not she did whisper the statement $S$ which the seated inhabitant, (#2), attributes to her.

• (i) #1 is a knave and does say $S$ : if she is a knave and did say $S$ then, since she is lying, there is/are either $0$ or $2$ knights among the inhabitants. Since she did say $S,$ #2 must be a knight, which means #3 must be a knave as he would be calling a knight a liar. This would leave us with a total of $1$ knight, which can't be the case since $S$ is a lie. Thus this scenario is impossible.

• (ii) #1 is a knave and does not say $S$ : this implies that #2 is lying and is hence also a knave, which in turn means that #3 is telling the truth and is thus a knight.

• (iii) #1 is a knight and does say $S$ : this would imply that #2 is also a knight since he is telling the truth. But this would mean that there are $2$ knights, (#3 would be lying and hence be a knave), contradicting statement $S,$ which is inconsistent with this option. Thus this scenario is impossible.

• (iv) #1 is a knight and does not say $S$ : this implies that #2 is lying and is thus a knave, which would in turn mean that #3 is telling the truth and must thus be a knight.

From this case analysis we see that in both of the two scenarios that are logically possible the seated inhabitant is a knave and the standing one is a knight.

(Note that we cannot make any conclusions about #1, as she could logically either be a knave or a knight base on the information provided.)

By the way that there exist an argument between the one sitting and the one standing, we can infer that there must be a truth teller (TT) and a lying liar (LL) between the two. Thus, amongst the three, there must be at least one and at most two truth teller present.

In the first scenario where there's only one TT between them, this sole TT would have been either one of the 2 men who argued, and it'd be impossible for the LL woman to tell the truth about it (of 1 TT present), and the conveyed message by the sitting man is clearly been tempered with.

For the second scenario with 2 TTs, the TT woman would have been honest and said just that, of there being 2 of them, so again, the middleman is intercepting once again, and this time it's the truth instead of a lie like what happened in the previous scenario.

Anyway, the seated one is a Lying-liar and the standing one is a Truth-teller.