@zig Either tap on the green button that says "Get started", or tap on the + icon in the upper right corner of the screen.
Follow the instructions on the screen. Make sure to keep the screen on and not to navigate away from the settings while the container is being created.
Might I ask why you want to install the lubuntu-software-center? As it is not touch enabled, it will probably not be a very pleasant experience to use on a phone.
The Libertine manager under System Settings is not the most user friendly either, but it does allow you to search for packages and install the ones you want from a touch enabled UI at least. It is not great for discovery, I will admit, but if you know what you are looking for, it is fairly easy to find and install.
You can also add PPA's via the user interface it provides.