Croatan was an Indian tribe invented by Hamilton McMillan, the head of the Democratic (Jim Crow) Party in Robeson County in 1885. He made up a story that they were connected with Sir Walter Raleigh's lost colony in 1587. He was a politician, not an historian, so he did not bother to explain what happened to the tribe between 1587 and 1885. He got the word Croatan from an island near Roanoke named Croatoan associated with the lost colony story.

He was not writing a history, just solving the problem of what to call light-skinned African Americans who had been free since colonial times, had a completely different culture from former slaves, and did not want to be associated with them. McMillan claimed the Croatans were descended from only friendly Indians and whites. In exchange for being called Indians and having their own separate school and own separate caste, they voted for Jim Crow legislation.
When whites in Robeson County began taunting them by calling them "Crows" (as in Jim Crow), they changed their name to Lumbee Indians.

Sometime after 1908 when the federal Dawes Commission started dividing land among Cherokees, it became popular throughout the Southeast for people to say they were Cherokees and there was a movement among some Lumbees to call themselves Cherokees.
Paul
Ps. Lawyers helped spread the word about the Dawes Commission since they were paid to file. Over 45,000 people filed for benefits, but there were only about 5,000 who were actually Cherokee. The 40,000 or so denied applications often contain perfectly true family history which prove that the applicant was never within hundreds of miles of a Cherokee settlement.