1.) Contact the New Orleans Public Library to search their Naturalization Index.This is described here: http://nutrias.org/info/louinfo/louinfo4.htmhttp://nutrias.org/info/louinfo/louinfo4.htm I would ask them to look up both Athas Stellius Lullias AND Arthur Baker in the Index.If he's listed, you can then go about getting his naturalization records, which hopefully will give you more information, including (hopefully! - sometimes very detailed, sometimes not) the date he arrived, ship, and place of birth.There is a fee of $3.00/per look-up.
2.) Order the death certificate of Arthur Williams, which can be done on the website of the Louisiana Secretary of State's website, Division of the State Archives.Just go here: http://www.sos.louisiana.gov/tabid/640/Default.aspxhttp://www.sos.louisiana.gov/tabid/640/Default.aspx Type in Williams, Arthur, Orleans Parish, and 1948, and he is the only one.There is a link for ordering information.Cost is $5.00, and it will hopefully list his parents, so you will hopefully be able to figure out if he was a cousin on the maternal or paternal side.Also, although the "place of birth" information may very well only say "Greece," sometimes you get lucky and actually have a hometown listed.