LiveReload is cool with file: URLs, unless you’re using a Safari browser extension, which does not allow that. (See: How do I choose the best integration method?)
We recommend Chrome over Safari for file: URLs. If, however, you prefer to develop in Safari with a browser extension, we recommend one of these approaches:
save your files as e.g.
~/Sites/something/foo.html, and view it as
http://localhost/~username/something/foo.html, where username is your short user name (don’t forget to also enable Web Sharing in System Preferences)
put a symlink into Sites folder to your project directory (you need to enable symlinks first as described here)