That part of it should only be necessary if you don’t have a reasonable distro already running on a desktop / laptop. Hence, for example, if your starting point is “only Windows” 
then you would indeed need to download PureOS for x86 and use Windows to “burn” that to a flash drive in order to do a Live Boot in order to do the whole reflash of the Librem 5.
On the other hand, if you already have a current e.g. Ubuntu version running on a desktop / laptop then you can use that directly.
I believe that @Sharon has a working desktop / laptop running a Debian-family distro.
Whatever distro you have, it will need a working git command and a working uuu command.
And you’ll need a good internet connection, since the download of the Librem 5 disk image is up to around 4 GB.
First of all, if you have anything worth saving on the Librem 5 as it is now then save it (e.g. copy some stuff from the main disk to the µSD card that you may have in the Librem 5). In fact, I chose also to use Jumpdrive to image the entire Librem 5 before reflashing (just in case). However that then adds to your workload.
Secondly, the previously linked official documentation for “reflashing the phone” does the whole job. Downloads the needed disk image, plus a few other needed files, and then invokes the uuu command, which is the command that effects the actual flashing.
One thing that I think is missing from the official doco … it does not invite you to choose between the encrypted variant and the unencrypted variant. To make this choice, the command
./scripts/librem5-flash-image
should have either --variant luks or --variant plain added to the end of the command. If you make no choice, from wandering through the Python code, it looks as if it defaults to luks, which is a good safe private default but may not suit everyone. (On the other hand, it is relatively painful to change from plain to luks or from luks to plain after the fact - so this is a choice that you want to think about and make before you start.)
And one other thing … if you don’t do the “udev” thing that is mentioned in the instructions then you will need to precede the above command with sudo
So, for example,
sudo ./scripts/librem5-flash-image --variant luks