I use rsync to make daily backups of my main machine's data files (mounted at /libdata) onto an external HDD (mounted at /backups/backdata, also on my main machine).

I have recently set up a second laptop (named Avalon) to mirror my main machine, and I copied all the /libdata files from the main machine onto Avalon by means of physically moving the external HDD from the main laptop to the Avalon mirror laptop.

More recently, then, I've configured both laptops with openSSH (server and client on both machines).

Now, with the external HDD re-attached to my main machine, I am trying to use an rsync command to mirror changes written to the backup onto the new laptop (which is named Avalon) as follows (executed from the main machine):

This rsync command successfully copies new and modified files as expected, but does not delete files that have been removed from the backup directories of the external HDD. (I've also tried replacing the rsync source directory with /libdata, but with the same failure to delete.)

I guess that is user permission related issue, but without details hard to say more.
Obviously not related directly to LAN.

Try to run the same command with the '--dry-run' option:

rsync -av --delete --dry-run /backups/backdata/ Avalon:/libdata | grep deleting

It will show you a list of files/directories rsync would delete if you ran it without the '--dry-run' option.