The second sentence is parallel.
In grammar, parallelism refers to having common elements that are repeated. Think of parallel lines, such as train tracks. When a sentence is parallel, some structural element is the same in both parts.
The first sentence is not parallel. This is why it sounds funny. You have “to punish them for wickedness,” where wickedness is a noun, and “being liars” which is not.
To be parallel, the sentence needs to read this way.
As blood oozes from the shoes, pigeons peck out their eyes to punish them for the wickedness and lying.
Notice that "for the ... lying" is a prepositional phrase. We need two nouns, compound objects of the preposition, not only to make the sentence parallel but to make it make sense.
Your second sentence is parallel, because it uses two infinitives: “to outsmart” and “to escape” in this case. Since both are infinitives, the sentence sounds a little better because there is parallelism, or the same pattern.