No naturalization record found yet for father.
And what's your point? I ask because there is now law that requires a person who lawfully immigrates to the United State to become a naturalized citizen. I know people from Ireland, Germany, Italy, and even Mexico, who are legal "green card" residents, but for whatever reason, have chosen not to become citizens.
You are exactly right. I know this from personal experience being a naturalized citizen, and having personally known dozens and dozens of people from European countries who for some reason do not wish to become US citizens. But since they are all Green Card (permanent residence visa) holders, they can exercise all the rights of a US citizen except vote. They can travel freely in and out of the country, collect social security and Medicare benefits if they have paid commensurate taxes.