Step 1: Understanding Lac operon.
The Lac operon in {E. coli} controls lactose metabolism and includes genes lacZ, lacY, and lacA.
Step 2: Enzymes involved.
$\beta$-galactosidase, permease, and transacetylase are products of Lac operon genes, while DNAase is unrelated to lactose metabolism.
Step 3: Conclusion.
Therefore, DNAase does not operate in the Lac operon.