I found a deposition in either 1638 or 1639 of a John Lilly who came to Virginia in 1637 on the Elizabeth of London
http://freepages.genealogy.rootsweb.ancestry.com/~cullember/otherfam/
1639deposition.html
and
http://image.lva.virginia.gov/VTLS/CR/04005/index.html
Survey report page 2 and page 3

Can You Trace Your Line To Robert Lilly ? yes

If you want to look up the lilly I have found in Suffolk my tree is available on ancestry gordon Paul lilly is anyone wants to have a look.
My grandfathers building firm Walter lilly is still in existence after 90 years. Although no longer owned by the family it is a major firm in and around London. Their 90 th birthday celebrations were held at the Tower of London