Lancaster Lovett, Jr - Family Connections

I haven't found a site that lists three consecutive Lancaster Lovetts. I found one that shows this Lancaster to be Lancaster I b. 1609 and married to Bathsheba, as the first of the American Lovett line.

Then I noticed that Ancestry trees have his info as:

Lancaster Lovett I
BIRTH18 April 1609 Astwell, Northamptonshire, England
DEATH15 Apr 1673 Norfolk, Norfolk, Virginia, United States

sources (14)records (13)photos (2)

Family Info

Father
John Lovett (1578–1633)

Mother
Elizabeth Josselyn (1584–1637)

If anyone has validation of his father being Lancaster Lovett I instead of John Lovett, please post that the source(s), etc. Otherwise, the father named John would fit with this Lancaster being Lancaster I and his son being Lancaster II instead of how they're currently listed, which I can't find any validation for there being three of them.

Thanks in advance for any assistance in getting their connections and details correct.