Here in the DR, nothing is called Lima, although "Lima" is the Spanish translation of "lime" they do not use that word here. Limes here are called Limon ( Lemons ).
Most names for citrus are just nick names. Limon Dulce ( sweet lemon ) which sounds like your description of Lima, Naranja Agria = Sour Orange, used for flavoring / cooking. Limon Criollo = same as Key Lime or Mexican Lime, in recent years the so called Limon Persia ( Persian Lime ) are being grown commercially.
I have a Lemon or Lime, tree of a variety I have never heard of, called a "Limon California" , like a Persian lime, but flavor more like an Lemon, so who knows maybe it is a lemon, but they do not turn yellow when ripe.
Valencia Oranges are known by the general public, but the rest are generally called either Naranja Dulce, or Agria. commercial growers are familiar with varieties though.
Seems to be a big mix up with citrus names, in Latin America.