How do I set a picture for my user on the login screen in Lubuntu 20.04?

There is a good guide for this on https://wiki.archlinux.org/index.php/SDDM#Installation

User icon (avatar) SDDM reads the user icon (a.k.a. "avatar") as a PNG image from either ~/.face.icon for each user, or the common location for all users specified by FacesDir in an SDDM configuration file. The configuration setting can be placed in either /etc/sddm.conf directly, or, better, a file under /etc/sddm.conf.d/ such as /etc/sddm.conf.d/avatar.conf.

To use the FacesDir location option, place a PNG image for each user named username.face.icon at the location specified by the FacesDir key in the configuration file. The default location for FacesDir is /usr/share/sddm/faces/. You can change the default FacesDir location to suit your needs. Here is an example:

/etc/sddm.conf.d/avatar.conf
[Theme]
FacesDir=/var/lib/AccountsService/icons/

I Just kept the pic I wanted in /usr/share/sddm/faces/ with the name <user-name>.face.icon As per the wiki it seems only .png files are supported.

This answer was provided in comment first by @yfluK

I'll suggest you look up the manual, ie. https://manual.lubuntu.me/stable/3/3.1/3.1.9/sddm_configuration.html?highlight=face%20icon

To change the picture for your user when you login simply copy the file you want as your user picture to in your home folder with the name .face.icon .

The file is located in ~ (your user directory)

sudo nano /etc/sddm.conf

Under block [Theme].

[Theme]
EnableAvatars=true
FacesDir=/usr/share/sddm/faces 

I named my picture my-user-name.face.icon, so I don't mix it with user-pictures from other users.