You don't need to translate it as, in this instance, it obviously refers to the parties.

Normally, "el justiciable" is the fact in question, requiring clarification and judgment.

justiciable (DRAE)
1. adj. Que puede o debe someterse a la acción de los tribunales de justicia. Dícese principalmente de ciertos hechos.

However, the same term may refer to one party (either party) or (more rarely) to both parties, as it means "deserving justice".