There was a book that came out a few years ago claiming that the Chinese reached North America in 1421. I saw the author interviewed on TV and he did not appear to be a raving maniac. I don’t think he used the Lee family of Virginia as evidence for the Chinese getting to North America.
"Chu," spelled various ways, is also a fairly common name in China. As evidence for his case, the author might also have cited Benjamin Chew, a politician and prominent jurist in colonial Pennsylvania.