- Some conditional claims are lies. ("If you show this car to any mechanic in town, he'll tell you it's a great deal.")
- Conditional claims do not express propositions (but, say, conditional probabilities).
- Assertions express propositions.
- So, not all lies are assertions.
Of course, (2) is a quite controversial theory of conditionals. And one can turn the argument around: All lies are assertions, so conditional claims express propositions (at least in those cases; but one can generalize from them). But if one thinks that the argument should be turned around in this way, then one must make the same move for every non-cognitivist theory, since it takes only one non-cognitivist theory in whose domain lies can be made to yield conclusion (4). For instance, one must reject non-cognitivism in metaethics and aesthetics. So far so good. One probably doesn't need to reject non-cognitivism about requests, on the other hand, since one doesn't lie with requests: "I'll have fries with that" isn't a lie when you don't want fries.
Are there domains where one can lie but where non-cognitivism is clearly right? I am not sure. Maybe something like talk of the spooky? One certainly can lie in something is spooky (e.g., to scare off a competing house buyer). But even there I am not convinced that the right conclusion is that not all lies are assertions. The right conclusion there may still be that we do in fact make assertions when we attribute spookiness.
Vagueness cases are another case to think about. I think propositions are always sharp, but we lie with claims that clearly do not express sharp propositions ("He was bald two days ago, but washed his hair with this shampoo, and now he's not"). But I don't think vagueness cases give one reason to accept (4). Rather, they lead to a refinement of (3): assertions don't express individual propositions, but something like a vague assignment of weights to propositions.
So overall, I don't know what to make of the argument.