The Golgi apparatus is the processing/packaging and shipping part of the cell (like the endoplasmic reticulum). It gets macromolecules ready and ships them out for use in the cell or secretion (exocytosis). The Golgi apparatus essentially modifies (via the different stacks of cisternae) and labels things like proteins and lipids for shipment (like a Post Office). Golgi apparatus uses sugar, carbohydrates and phosphates to process the material before shipping.
Lysosomes are created by the addition of hydrolytic acid to endosomes from the Golgi apparatus. Basically, the Golgi apparatus receives protein enzymes from the ER, which are packaged in a vesicle in the Golgi apparatus, processed and finally, pinched off as a Lysosome. Lysosomes then float in teh cytoplasm until they're needed.
Lysosomes rely on enzymes created in the cytosol and the endoplasmic reticulum. Lysosomes use those enzymes (acid hyrolases) to digest food and 'take out the garbage.' Golgi (and the ER) is the shipping department and lysosomes (packages or trucks) either digest the shipments for use in the cell or they become the garbage truck.
To simplify the above answer: lysomes are proteins covered in a vesicle film that are shipped to the cytoplasm by the either golgi bodies or the endoplasmic reticulum