The term “lefty specialist” has a certain connotation to it. That is, it’s a lefty who has a nasty breaking pitch (usually a slider) that is hard for opposing left-handed hitters to contact. Also, they don’t typically throw that hard, but there are some who do.
The Dodgers traded Paco Rodriguez in the Hector Olivera deal. When they did so, they traded their best left-handed reliever with a fastball-slider combination. They got back Luis Avilan, who relies mostly on the changeup but also has a curveball.