The answer is to recompile the Litecoin daemon, making sure to call the configure script with the --enable-wallet option:
./configure --enable-wallet
From there, make and make-install will give you a binary that has the getnewaddress RPC method available.
This reason behind this is that - instead of just disabling the methods around using the daemon as a wallet, or throwing an error in the case they're used without the --enable-wallet compilation option - the methods themselves are not compiled into the binary at all. This is likely due to the use of litecoind as a wallet requiring an extra library - the Berkeley DB library - and the path of least resistance being to not try to compile that section of the code at all in order to avoid issues with referencing the library, but that's conjecture.
This should also solve similar issues in other coins forked from the bitcoin source, and for bitcoin itself.