Step 1: Identify the substrate and products for each enzyme.
A. \(\beta\)-galactosidase: This enzyme, also known as lactase, hydrolyzes the disaccharide lactose into its constituent monosaccharides. This matches III. Galactose + glucose.
B. Lecithinase (Phospholipase): This enzyme breaks down lecithin (a phospholipid). The products include a diglyceride (fat), phosphoric acid, and choline. This matches I. Choline + H$_3$PO$_4$ + fat.
C. Urease: This enzyme catalyzes the hydrolysis of urea into ammonia and carbon dioxide. This matches IV. CO$_2$ + NH$_3$.
D. Lipase: This is an enzyme that breaks down fats (triglycerides) into their components. This matches II. Glycerol + fatty acids.
The correct set of matches is A-III, B-I, C-IV, D-II.