I don't think lying about why I don't drink is a good idea for me. If someone were to press as to why I don't drink, I'd say - "I just don't want any."
I also don't believe it necessary to answer questions I don't want to answer.
I've only had one person ever ask me why I don't drink, so I don't believe that is much of a stumbling block. She herself was a heavy drinker.