Similarly to what I wrote for Fedora 29, here is how I was able to create a Fedora 31 LXC container on an Ubuntu 18.04 (bionic) laptop.

Setting up LXC on Ubuntu

First of all, install lxc:

apt install lxc
echo "veth" >> /etc/modules
modprobe veth

turn on bridged networking by putting the following in /etc/sysctl.d/local.conf:

net.ipv4.ip_forward=1

and applying it using:

sysctl -p /etc/sysctl.d/local.conf

Then allow the right traffic in your firewall (/etc/network/iptables.up.rules in my case):

# LXC containers
-A FORWARD -d 10.0.3.0/24 -m conntrack --ctstate RELATED,ESTABLISHED -j ACCEPT
-A FORWARD -s 10.0.3.0/24 -j ACCEPT
-A INPUT -d 224.0.0.251 -s 10.0.3.1 -j ACCEPT
-A INPUT -d 239.255.255.250 -s 10.0.3.1 -j ACCEPT
-A INPUT -d 10.0.3.255 -s 10.0.3.1 -j ACCEPT
-A INPUT -d 10.0.3.1 -s 10.0.3.0/24 -j ACCEPT

and apply these changes:

iptables-apply

before restarting the lxc networking:

systemctl restart lxc-net.service

Create the container

Once that's in place, you can finally create the Fedora 29 container:

lxc-create -n fedora31 -t download -- -d fedora -r 31 -a amd64

To see a list of all distros available with the download template:

lxc-create -n foo --template=download -- --list

Once the container has been created, disable AppArmor for it:

lxc.apparmor.profile = unconfined

since the AppArmor profile isn't working at the moment.

Logging in as root

Starting the container in one window:

lxc-start -n fedora31 -F

and attaching to a console:

lxc-attach -n fedora31

to set a root password:

passwd

Logging in as an unprivileged user via ssh

While logged into the console, I tried to install ssh:

$ dnf install openssh-server
Cannot create temporary file - mkstemp: No such file or directory

but it failed because TMPDIR is set to a non-existent directory:

$ echo $TMPDIR
/tmp/user/0

I found a fix and ran the following:

TMPDIR=/tmp dnf install openssh-server

then started the ssh service:

systemctl start sshd.service

Then I installed a few other packages as root:

dnf install vim sudo man

and created an unprivileged user with sudo access:

adduser francois -G wheel
passwd francois

I set this in /etc/ssh/sshd_config:

GSSAPIAuthentication no

to prevent slow ssh logins.

Now login as that user from the console and add an ssh public key:

mkdir .ssh
chmod 700 .ssh
echo "<your public key>" > .ssh/authorized_keys
chmod 644 .ssh/authorized_keys

You can now login via ssh. The IP address to use can be seen in the output of:

lxc-ls --fancy