From the experts:
Adlai is an Old Testament name long associated with 1950's liberal presidential candidate Stevenson, who was named after his grandfather, who was Grover Cleveland's vice president in the nineteenth century. Now it's an unusual Biblical choice ripe for rediscovery.
In the Bible, Adlai was a minor character, the father of one of King David's herdsmen. Adlai is a contracted form of the Hebrew name Adaliah.