Like I said I wish it was true.I suggest you read the back of your book.It says:
I will quote from my source which is "The Americans of Royal Descent" by Charles H. Browning, Seventh Edition. This is from page B of the Corrigenda (which is in the back of the book). "LYMAN.Pedigree XXXVI.-This claim is reproduced from Dr. Coleman's "Lyman Genealogy." It seems that Sir "William" Lambert, of Owlton, and his wife, Lady Joan de Umfraville, had no son named "Robert," and that the "Robert Lambert, of Owlton," his alleged son, was the son and heir of Sir John Lambert, of Owlton, the son and heir of the said Sir "William," by Lady Joan. Since printing this claim to royal descent, I find that there is some uncertainty about it, because there is no evidence, and only assumption, by Dr. Coleman, that Henry Lambert, of Ongar, in Essex, 1447, was the son of Robert Lambert, of Owlton, in Durham. I am retaining the claim, hoping that it may be substantiated. See further as to it in the "Boston Transcript," 16 May, 1904".