There is currently no remote (LAN) live preview in Brackets and there are open issues on Github for the feature request. (Here's one for example)
The livedev.multibrowser
option described in the currently accepted answer opens live preview to multiple browsers on the same machine but does not allow access from anything other than localhost.
Here's a workaround that I've been using in the meantime:
Make a standard local web server (with Node/Apache/IIS/whatever) and install and run LiveReload on your dev machine for your project. On the remote machine(s) install the LiveReload browser extension, visit your site and turn on the LiveReload plugin. You don't get the instant (saveless) updates of the Brackets live preview, but the page will auto-refresh on remote machines when you save any files inside your project.