Following are some links that might be of help:
Contra Costa Historical Society: http://www.cocohistory.org/index.html
Contra Costa Genealogical Society: http://www.cccgs.org/
Contra Costa Databases on Rootsweb: http://www.rootsweb.com/~cacccgs/
California Genealogical Society: http://www.calgensoc.org/web/cgs/cgshp.nsf?Open
There are also some websites specifically associated with the Lima surname that you might want to explore:
Sorry I don't have anything more specific for you. Hope this is of some help.
Tormey Family History Website