You can see from the slide above that there is no one Liberty profile. Each of the traditional implementations has it's own Liberty profile plus there is a single standalone one too. Think of Liberty as a lightweight implementation of each model. So what's really important to understand is the requirement in order to under which model is required.
While Express isn't listed here I can tell you that it is not free so these look like the only options available on Cloud.
As helpful reminders for you or to share your thoughts with others