Answer
This case of convergence might involve the same changes because the enzyme lysozyme may be so critical and with so few possible changes that those which have appeared convergently are the only ones possible.
Work Step by Step
The convergence seen in vertebrates' wings can happen because many parts in the forelimbs can change to produce a functional wing. However, an enzyme like lysozyme, which is highly conserved, is limited in what changes can occur and still have it retain its required function.
