They re in fact the same image, as you can verify by comparing their digest:

$ docker pull ghcr.io/linuxserver/plex
Using default tag: latest
latest: Pulling from linuxserver/plex
Digest: sha256:476c057d677ff239d6b0b5c8e7efb2d572a705f69f9860bbe4221d5bbfdf2144
Status: Image is up to date for ghcr.io/linuxserver/plex:latest
ghcr.io/linuxserver/plex:latest
$ docker pull lscr.io/linuxserver/plex
Using default tag: latest
latest: Pulling from linuxserver/plex
Digest: sha256:476c057d677ff239d6b0b5c8e7efb2d572a705f69f9860bbe4221d5bbfdf2144
Status: Image is up to date for lscr.io/linuxserver/plex:latest
lscr.io/linuxserver/plex:latest
$

See how both images have the digest sha256:476c057d677ff239d6b0b5c8e7efb2d572a705f69f9860bbe4221d5bbfdf2144. Since the digest uniquely identifies the exact content/image, that guarantees that those images are in fact byte-for-byte identical.