In “Zayd is a lion,” both the mushabbah and the mushabbah bih are expressed. The sentence makes a forceful claim of likeness; it does not simply omit Zayd and replace his name by “lion.”
By contrast, in “I saw a lion shooting arrows,” where the context determines that a human is intended, the man's name is absent and the word “lion” has been transferred to refer to him.
Analytical test: the presence or absence of “like” is not decisive by itself. Ask whether one term has been borrowed as the name of the other, or whether two expressed terms are brought together in a forceful predication of shared quality.