It all depends on their personality. Personally, i don't think that Hermione's personality would be shown through a cocker spaniel. What about the cocker spaniel is simlar to Hermione's personality? Yes, Severus' animal form could be a lion, but i don't think that is the form it would take. You need to dig deep into Severus' personality, and you'll get his animagus.
New question. What steps do you think would be involved in becoming a Animagi?