If you search for proxmox "unable to install initramfs", you will find several results. This is a proxmox issue, and I dare to guess that the problem is with the too little available space in the LXD VM for proxmox. I think the default disk space for a LXD VM is 2GB or so.
You can check if diskspace is the issue, if you run the following command after you lxc init.
Exactly as you said, insufficent disk size was issue… I was somehow convinced that default size is 20GB, but after rewatching recently published video made on LXD Youtube channel, I realized default is 10GB… Many thanks for your help!