Answer:
Jax will pay for (his) lunch with cash today.
Explanation:
"His" is not a pronoun. It is a possessive adjective: my, your, his, her, its, our, your, their. It is called so because it precedes a noun and modifies it. Therefore, if you say "his" lunch, it is not about any lunch; it is rather a specific one, belonging to a particular person.
The antecedent of "his" is "Jax", since "his lunch" refers to "Jax's lunch", that is, Jax is the person whose lunch we are talking about.
