Naturalness and Projectibility II
Brian Weatherson tells me that Lewis does mention Goodman's 'New Riddle' as a task for natural properties in "Meaning without use: Reply to Hawthorne". Lewis says here that we should not be scared off by "Kripkenstein's challenge (formerly Goodman's challenge)" to find a distinction between natural and unnatural extrapolation (p.150 in Papers in Ethics and Social Philosophy, similar remarks can be found in the introduction to Papers in Metaphysics and Epistemology). So the first suggestion is very probably right.
(Reading Brian's comments it now seems to me when I argued that natural properties can't solve the New Riddle I've been confusing it with the Old Riddle. All the New Riddle requires is an objective distinction between good and bad extrapolations. That induction based on good extrapolations might nevertheless yield systematically false predictions ("not work") is the Old Riddle.)