How secure is this use of Ziv-Lempel encoding?
Ziv-Lempel is a data compression algorithm, so in general it doesn't protect your data. As for your question: 


  More generally, how difficult is it for an adversary to distinguish two strings which have been Ziv-Lempel encoded but not encrypted?


An adversary just can decode two strings and compare them. Due to the fact that Ziv-Lempel is an encoding algorithm, if you send your data to somebody then you have to send the other information needed to decode your data by the receiver. So, in this case an attacker can easily get access to the transmitted data.