Final answer:
Option (1), The liver synthesizes bile, which emulsifies lipids and aids digestion in the small intestine, making it the correct answer to which organ facilitates the mechanical digestion of lipids.
Step-by-step explanation:
The organ that synthesizes a compound facilitating the mechanical digestion of lipids is the liver. The liver produces bile, which contains bile salts and phospholipids that are crucial in the emulsification of lipids.
This emulsification process breaks down large lipid globules into tiny lipid droplets called micelles, significantly increasing the surface area for the enzyme pancreatic lipase to act upon. As a result, the digestion of lipids is greatly enhanced in the small intestine.