Info on her parents seems hard to find, but Supermanica (the Superman Wiki)
article on Lana does indeed list her father as
Professor Lewis Lang , "a noted archaeologist."
Mother's name is Sarah, and the stub on Lewis mentions that there's at least one brother (though no name is given).
Oh, and since it mentions that Lana's uncle is
Professor Potter , I guess we can assume that's Sarah's maiden name.