Regarding your edit: "Lawful permanent resident" does not include US citizens. It is a term of art in US immigration law that denotes what most people call "green card holder." For example, the US Department of Homeland Security has a page, Lawful Permanent Residents (LPR), which begins by saying:
Lawful permanent residents (LPRs), also known as “green card” holders, are non-citizens who are lawfully authorized to live permanently within the United States.
User102008's answer is correct; US citizens do not need eTA, and in fact they cannot get it. If you try to apply for eTA, after you indicate that the country code in your passport is USA, you see this message:
As a U.S. citizen, you are exempt from the eTA requirement. You do not need an eTA to travel to Canada. Make sure to travel with valid proof of U.S. citizenship such as a passport and other acceptable travel documents.
At that point, it is not possible to proceed with the eTA application.