Reading the Apple documentation it seems mandatary to use Photoshop CC 2014 or 2015 to create the parallax for icons and images for tvOS store. Is possible use another tool or we are forced to use Photoshop?
You don't need to deal with .lsr file at all. You just need to have separate PNG file for each layer, and construct the "App Icon - Small" with them in the asset file. Xcode even gives you a nice Parallax preview.
Therefore, you don't need to use PhotoShop at all. Any app that can deal with PNG files (even the Preview app of OSX) is sufficient.