I have discovered through a very reputable geneologist that the Lima Family settled in Galicia, Spain and established De Limia in 409 AD, not far from the river Lima. They established commerce and spoke Portuguese. They are Celtic people as well because they established as Galicians, married etc., and their Portuguese is of Gaelic origin. The Spanish conquered the Northwest corner of the Iberian coastline 500 years ago, taking it away from Portugal.
It is a very old Family. They speak Spanish, Galician (form of Galic), Portuguese and of course helped settle the Americas, i. e. Lima, Peru, speaking Portuguese and Spanish. My GreatGrandfather many generations ago, around the late 1600s owned ships and sailed them out of the Azores.
I learned of a Sicilian root 20 years ago from another geneologist, but for all intents and purposes, they have their real history in the land of Celts, Galicia, Spain, and migrated to the Americas.