Yes some clarification that may help.
There is wordpress.com which is a wordpress hosting / web package all in one. You do not need to delete this account, however it wont work with Lay Theme unfortunately.
If you go to wordpress.org ( i know a little confusing ) you are able to download the free program; "Wordpress ( CMS or: content management system ).
This is free software and separated from Wordpress.com the hosting/account service.
Many websites use "wordpress" the CMS and install it on their domains, in fact many hosting providers E.g dreamhost - have "one-click installs" to add to your website.
As stated on Lay Theme's installation page: https://laytheme.com/installation.html
Lay Theme will work on any Wordpress except the specialised wordpress.com / hosting package all in one version.
Hope this provides some helpful insight @hugak it can be confusing i know with how Wordpress the company has structured this .com / .org situation.
Sincerely Richard