The Lees of Virginia are pretty much covered by other projects, such as Notables, 1776, Civil War, etc. A lot of work has been done on this family due to a lot of "fabrication" of lineages over the years. You may find that you are a part of one of those lineages.
I, too, was told about a "relationship" to the Virginia Lees which started me on my genealogical journey. I have proven that we are NOT related, only to be confirmed later by DNA.
I will warn you that autosomnal DNA results in this family are so skewed by fabricated lineages that I would not use it. My brother and several 2nd and 3rd cousins have done YDNA, and when you compare their DNA to other test takers with valid Virginia Lee lineages, there is no relationship. The DNA issue is part of the HOT topic that RJ refers to. If you need some help with research, let me know. I have done alot of Lee research.