Final answer:
The Golgi apparatus is responsible for the formation of both lysosomes and vesicles, with proteins from the rough endoplasmic reticulum being sent to the Golgi for modification, sorting, and packaging into vesicles (option 2).
Step-by-step explanation:
The organelle that gives rise to both lysosomes and vesicles is the Golgi apparatus. Proteins and other molecules synthesized at the rough endoplasmic reticulum (RER), which is adorned with ribosomes, are transported to the Golgi apparatus. Here, they are modified, sorted, packaged, and then dispatched to their destination within vesicles. When these vesicles contain enzymes destined for a lysosome, they are referred to as lysosomal vesicles. These vesicles play various roles including digestion and waste processing within the cell.
It is through the Golgi apparatus that enzymatic proteins are packed into new lysosomes. The formation of secretory vesicles, which can be involved in exocytosis, and lysosomes, which assist in cellular digestion, occurs as a result of the modifications and packaging processes within the Golgi apparatus. The entire system, including ribosomes, RER, vesicles, and the Golgi apparatus, contributes to the protein synthesis and transportation within the cell.
So, the answer is (option 2).