I found what may be Virginia Verret on the 1900 census. There is a Virginie Verret [18, bn 4-1882] who is listed as a niece in the household of Cesaire Dugas  and his wife, Endolie Dugas . They are at Fausse Pointe in Iberia Parish.
If you are in Louisiana, I suggest that you may want to look at Father Hebert's Southwest Louisiana Records. It is a set of books containing the BMD records for the area and Iberia Parish would be included. Right off hand I don't recall the dates included, but you may be able to find something. Also, any marriage records for the parish may be of use. A.D. Lee and Virginia Verret would have been married prior to 1914. Also, that Virginie who was born in April of 1882 should be listed in the book.
I still find nothing on the 1920 census. If the parents were already deceased by 1920, the two children should be listed. I checked all the Mary/Marie/Maria listings for 1920 and none appear to be the correct one. Finding the boy is more difficult since we don't know his first name.
I presume that you don't know of any Lee or Verret connections in your family. Maybe finding who Virginie's mother was may give you a lead.