Just to clarify a few things.
WebSphere Liberty is free for development purposes.
For production you may use version downloaded from wasdev.net for free (without support), if the heap size doesn't excess 2GB in the whole organization you are working. See details about that here What the Liberty runtime license lets you do
For any other versions like Liberty Core, Base, ND, or z/OS you need a valid WebSphere license.
So for example, if you already have WebSphere ND license, you can use Liberty instead of full WebSphere.
If you don't have any WebSphere licenses and you would like to use WebSphere Liberty in production you have to buy licenses, see here WebSphere Application Server family
Trial versions are only for 60 days.