As per my understanding, in Launch we do have the option to host the Launch library either on Akamai server i.e. Managed by Adobe or you can opt for the self-hosting option using which you can host your Launch library in your own server. For more information on self-hosting, you can refer to the below documentation link.
Also, I would like to inform you that as per the current architecture of Analytics we allow the users to use the self-hosting option to host the Launch library but we don't have any self-hosting option to host the Analytics data on any other server.