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"Welcome home, my son." - Jor-El, to Clark Luthor, Kent

Jor-El is an artificial intelligence. His nature, purpose and backstory can be assumed to be roughly the same as his Earth-1 counterpart's.

Season Ten

On Earth-2, Clark Luthor was able to create the Fortress of Solitude, but his adoptive father Lionel Luthor suppressed Jor-El's essence in the Fortress using electronic equipment, as Clark Kent discovered when he was sent to Earth-2 after activating the mirror box.

Later, after the Jor-El of Earth-1 transported him to the Fortress of Earth-2, Clark Luthor approached the Fortress' Console and called out to his Kryptonian father, who welcomed his son home, revived by the effects of the Jor-El of Earth-1.

In the Comics

The Earth-Two/Golden Age version of Jor-El was named Jor-L and first appeared in Superman #53 (August, 1948). He sent his son, Kal-L, to Earth, when Krypton was destroyed.