Tiled is really great. I'm using it in a project that I occasionally poke at as well, only with Love2D, and as a sidescroller sort of project. I was impressed by how easy it was to set it up to work with my game in spite of how generic it is.
The functionality to export directly to lua source files was a particular treat, though there are probably situations where you'd want to still just use json or one of the other formats supported by Tiled even when working in a lua project.
I'm not sure if it's the proper method, but I actually did implement parallax in my project, though I just did it by essentially creating a layer which I marked as parallax and then had my game draw it with a parallax offset from the rest of the map depending on the camera position.
The functionality to export directly to lua source files was a particular treat, though there are probably situations where you'd want to still just use json or one of the other formats supported by Tiled even when working in a lua project.