I posted something similar in another thread. It isn't always number of generations. Sometimes it is years. In addition, if there is a living relative in between that would be eligible for some countries that extends eligibility.

For example when we found some of the parish records for my wife's family in what is now Poland were listed as translated from Lithuanian, that opened the possibility of establishing a link with Lithuania for her. However, we didn't pursue it further.

Some countries it is if you could prove descent from somebody living in that country on or after a certain year.

Others it is proving a link regardless of years.

EDIT: Long time in the US doesn't always mean not eligible - my wife's family tree would put her eligible for Daughters of the American Revolution, Daughters of the Confederacy, and potentially 2 EU citizenships.

Also double check any answer you get. My father was born in the UK, and was a UK citizen. He passed away when I was young however. I was told in the mid-1990's that the oath for US Citizenship was considered officially denouncing his UK citizenship. I was told this after calling one of the UK government help lines. However, found out just a couple years ago that it was not considered as such unless he had written a letter to the UK Home office stating he was renouncing it. I have since obtained my UK passport as proof of my UK citizenship.