Language Use Without Conventions
So Lewis says that a language L is used by a population P iff there prevails in P a convention of truthfulness and trust in L.
This requirement for language use seems far too strong, given Lewis's account of conventions.
The most obvious problem is the condition that for a regularity to be a convention, it must be common knowledge in the population that it is a convention. Lewis offers some weak readings of this condition, but even his weakest versions rule out that sufficiently many members of the population may doubt or deny that the regularity is a convention. So if there were sufficiently many French speakers who believe that their language is completely innate, they would not partake in the convention of truthfulness and trust in French, and thus not use French, on Lewis's account. It even suffices if sufficiently many French speakers merely believe that there are enough who believe that, or believe that there are enough who believe that there are enough who believe it.
Other problems are raised by Lewis' condition that if R is a convention then the belief that everybody else conforms to R gives everybody a "good and decisive" reason to conform to R herself. Does the belief that everybody else is truthful and trusting in French necessarily give me a good and decisive reason to be truthful in French? Couldn't it be even better for me to be untruthful in French given that the others will believe what I say? Perhaps we are often truthful not because the others are truthful and trusting, but because we fear social sanctions. Language use then is more like a socially enforced regularity of cooperation in a prisoner's dilemma than a convention a la Lewis.
Finally, there's the condition that for R to be a convention, there must exist an alternative possibility R' such that everybody would prefer to conform to R' given that the others conform. Couldn't there be language use in a population where tough laws prohibit the use of any language other than the state language? Then there wouldn't exist a convention of truthfulness and trust in this language on Lewis' definition. (If I recall correctly, Andreas Kemmerling once made this point.) And what if those French people were right who believe that their language is innate? Would we no longer say that they use French?
So Lewis' requirement for language use is too strong. The same is true for many alternatives, e.g. those emphasizing the social enforcement of conventions (like Kemmerling, von Savigny, and Gilbert): Surely a community of kind and tolerant people could use a language even if they never objected to or otherwise sanctioned nonconformity with the rules of language. More generally, the possibility of innate languages shows that any analysis of language use in terms of conventions is too strict.
Does a mere regularity of truthfulness and trust, or of truthfulness alone, suffice? Consider a tribe of Martians who show exactly the same linguistic behaviour as speakers of French on Earth: They usually utter "il pleut" only when it rains, "il neige" when it snows, and so on. They are truthful in French. But their utterances aren't used for communication. For in fact, they communicate by some telepathic process. The French sounds are accidental by-products of those process. Do they use French? I think not. So a commonly known regularity of truthfulness and trust in French doesn't suffice. (We have trust because the Martians know that "il pleut" is a by-product of the telepathic process used to transmit the information that it rains. Hence they know that it probably rains when this by-product occurs, but they never infer that from its occurrence, because its occurrence is always trumped by the more reliable and simpler telepathic process.)
I'm not sure just where to draw the border. In view of the endless and useless controversies over whether this or that kind of animal uses language I'd guess the border lies somewhere around there. But that doesn't help much. Moreover, once the requirement of possible alternatives is jettisoned, and thereby the 'arbitrariness' of linguistic tokens, it becomes difficult to distinguish language use from the use of natural signs to convey information.
Which brings me to Grice and another problem with lifting Lewis' requirements: The more conditions we drop from Lewis' account, the more we lose of its attractive consequences. For instance, only the strong condition on common knowledge of language conventions allows Lewis to derive the Gricean (and even Strawsonian) mechanisms. Only his strong conception of language use allows him to elegantly explain it as a rational means to convey information.
Perhaps it would be better not to understand Lewis as offering necessary and sufficient conditions for any kind of language use. (Though he says he does.) Perhaps he rather offers a theoretically rich account of one particular kind of language use, one of which he believes that it comes close to what humans actually do with their languages.
A proper analysis of languages use in general would be much weaker, much fuzzier, and would probably contain indexical elements: If it turns out that our languages are all innate (those who think they have learned second or third languages have been deceived by evil demons), we certainly wouldn't say that we don't use language. But if it only turns out that some Martians use something innate that looks like language, that conclusion isn't so clear.
For it to be common knowledge that a convention prevails in a language, surely people don't have to explicitly subscribe to the view (i.e. be disposed to assert) `language is conventional'. Rather, each of the parts of the analysis must be common knowledge: that there is a regularity, that general conformity is preferable etc etc. It's the theorist who classifies this common knowledge as common knowledge about a convention. (I guess this is one of the `weak readings' you mention---but then I don't see why the condition isn't met).
Connectedly, why should the conventionality of language be incompatible with innateness? Isn't that just a particularly good way of latching on to one solution to the coordination problem? (Of course, one Lewisian condition on conventionality of a regularity is that there be some other regularity that would do just as well... but that's surely true even if the language is innate---if we were to have some other language innately, it'd be fine.).