Error initializing network controller: failed to create NAT chain DOCKER: iptables failed: iptables -t nat -N DOCKER: iptables v1.8.4 (legacy): can’t initialize iptables table `nat’: Permission denied (you must be root)

I am not sure how that contradicts my suggestion using the official documentation. You can use it to install Docker on previous versions of Ubuntu, although as I wrote in the other topic Docker works on Ubuntu 22.04 too. We can continue the discussion about that there if you want to, but you can choose to install Docker on previous supported Ubuntu versions. If you are interested in LXC, I can recommend you the following topic where I wrote about that too

It was about a different issue, but it might be related somehow. Note that although we mentioned “proxmox” multiple times, when I installed Docker in LXC container, I used a simple LXC on my laptop.