This is a military patch originating from the 504th flight test squadron, operating out of Groom Dry Lake, and Los Alamos AFB. Most of these projects are classified, and bearers of this patch are prohibited from discussing their occupation, hence, "A Lifetime of Silence". In a 1930's novel and a 1980's pornographic film, they both have green doors that a character cannot gain access to. In addition, the military, and most banks, use green vaults. So, the Green Door could be referencing that there are secrets that the public dosen't have access too. The true meaning of this patch is currently classified, and most likely will not be declassified in our lifetimes.
A lifetime of silence, behind the green door is the motto of the 504th Flight Test Squadron...
by AFC. Stanoff May 13, 2012