Is there a way to hide certain information from unprivileged containers? For example, hiding the output of lsblk?
Not really, no. That’s information that anyone on the system gets access to, even a completely unprivileged nobody user.
As root in the container you can try masking part of /sys with bind-mounts and the like which would be enough to prevent an unprivileged user in the container from seeing some of those files, but that’s about all you can do.