This is a very interesting history on the family. My name is Dan Lima and my grandfather Antonio Barcelos Lima came from Terceira, Azores. He settled in California and died in Los Banos. All that I know is that there must be tons of Lima's that came from Terceira. Somehow, I'm sure that we're all related, but I haven't found the missing pieces yet.
All that I can tell you is my lineage: Dan Lima (me) (1977-current), Joe Lima (1955-current) , Antonio Barcelos Lima (1925-1995), Antonio Lima (1888-1970), Antonio Lima (1866-?), Manuel Lima (?-?).
If any of these men fall into your lineage, please tell me so we can try to figure out how we Lima's are all related. Dan Lima