Lysosomes may originate directly from the endoplasmic reticulum, or from the Golgi membranes, and then associated with vesicles which have arisen by pinocytosis or phagocytosis. Protein granules synthesized by the ribosomes are seen in enlargements of the endoplasmic reticulum.. These if budded off, would give rise to bodies having the characteristics of lysosomes. There is also evidence that the lysosomes originate from the Golgi complex. It is possible that the Golgi complex buds off primary lysosomes containing hydrolytic enzyme. The lysosomes are so called because they contain lytic or destructive enzymes. The lysosomes show polymorphism in different cell types, and even within a single cell.
Lysosomes are similar to vesicles in that they contain digestive like enzymes that break down anything that the cell does not need. Lysosomes also break down nutrients. One that unwanted or unnecessary material is broken down, then the vesicles will transport that material outside the cell. In the case of broken down nutrients, vesicles will form and transport those nutrients to the areas of the cell that needs them. I hope that answer your questions. Basically: Lysosomes break down things. When done, vesicles transport those broken down materials out of the cell or where the cell needs them. That's how they work together to mantain homeostasis within the cell.