Step 1: Understanding turnover number.
Turnover number (k\(_\text{cat}\)) of an enzyme is the number of substrate molecules converted to product per enzyme molecule per second under optimal conditions.
Step 2: Compare enzymes.
- Penicillinase: High k\(_\text{cat}\), rapidly hydrolyzes penicillin.
- Chymotrypsin: Protease with relatively high turnover rate.
- Tryptophan synthetase: Moderate catalytic rate.
- Lysozyme: Catalyzes hydrolysis of glycosidic bonds in bacterial cell walls, but very slow, low k\(_\text{cat}\).
Step 3: Conclusion.
Therefore, among the options, Lysozyme has the lowest turnover number.