It is not possible to run Launch entirely on premise. However, you can self-host your Launch library on your own system or any system of your choice. You do this by creating a Self-managed adapter. I've posted the documentation for this below:
There are a number of reasons to choose to host your own build files.
Organizations have a number of security and legal requirements that might make cloud-hosting a less-desirable or impossible option.
You can reduce the number of required DNS lookups by hosting your own files.
You might prefer to have more control over edge locations, caching, and so on.
To meet these requirements, Launch allows you to push your completed builds to an SFTP destination.Launch connects to an SFTP site using an encrypted key. To use this connection type:
Your SFTP server must generate a key
You must provide the username and encrypted private key during the adapter setup process
If you select an SFTP adapter for your environment, there is an additional path variable that you'll need to provide to the environment. This path field is the HTTP path to where your build files are stored relative to your web site. This field is required because the different files in the build reference one another. Launch needs to know where they will are so the files can reference each other properly.