Are the Golgi apparatus and lysosomes related?

Yes, lysosomes are formed by the fusion of endosomes with transport vesicles that have budded from the trans Gogli network (TGN). During endocytosis, a portion of the plasma membrane invaginates and pinches off internalizing extracellular materials in vesicles known as endosomes. As these endosome mature into late endosomes they fuse with transport vesicles from the Golgi apparatus that contain digestive enzymes (e.g. acid hydrolases). Lysosomes arise as a result of their fusion, and the extracellular content is degraded by acid hydrolases.