I've always thought that android was developed by Google.
It is, partly. It is developed by a consortium of developers know as the Open Handset Alliance, of which Google is the largest member. Once development of a new version is completed, it is published to the Android Open Source Project, which as the name suggests, is open source.
There are multiple projects which build upon the open source code, and end up with a more privacy or security focused product. Examples include GrapheneOS and LineageOS, which you mentioned.
To the tech experts, is it possible to uninstall the google version on our android phones and install it with the LineageOS as mentioned in the article?
Yes. You will find instructions for how to do so on their respective websites:
https://wiki.lineageos.org/devices/ and
https://grapheneos.org/install.
Be aware that doing so is not without risk. It is possible to brick your phone if you make mistakes while installing a custom OS.