The usual English translation seems to be Region.
For example, Wikipedia has an article on the Lima Region, within which are 10 provinces.
And the CIA Factbook says that Peru's administrative divisions are, "25 regions (regiones, singular - region) and 1 province* (provincia); Amazonas, Ancash, Apurimac, Arequipa, Ayacucho, Cajamarca, Callao, Cusco, Huancavelica, Huanuco, Ica, Junin, La Libertad, Lambayeque, Lima, Lima*, Loreto, Madre de Dios, Moquegua, Pasco, Piura, Puno, San Martin, Tacna, Tumbes, Ucayali"
(The CIA seems to have lost track of the exact count, or counted the Lima Province as a region, where Wiki says that it is a province not part of the Lima Region or any other Region)
Further information from the Wikipedia article on the administrative divisions of Peru:
Peru was divided into 24 departments (departamentos; singular: departamento) until the creation of the regions in 2002. These regions are governed by Regional Governments. Many people still use the old departamentos term when referring to the current regions of Peru, although it is now obsolete. The departments were identical to today's regions, with the exception of two new regions (Callao and Lima).
So it appears that the historical departmentos were translated as "departments". But the current division into regiones are called "regions" in English.
If you want to talk about the historical departamento I'd call it either "Lima Department", or "The Department of Lima" in English.