Does Jason Grace die in The Lost Hero?

He was in a relationship with Piper McLean until she broke up with him because their relationship felt “forced” and was largely orchestrated by the marriage goddess, Hera. A couple of months later, he died at the hands of the third emperor, Caligula, when fighting aboard his yachts.

What does Piper do when Jason dies?

Sometime later Piper breaks up with Jason due to feeling that their relationship was forced onto them by Hera and her mother and wanting to live for herself even though later after he dies, Piper states that she still loved him.