The Lisqual were Betrisian citizens of one of the larger and more prominent provinces of planet Betrisius III. The Lisqual were apparently responsible for the planetwide network which controlled Betrisius' population of convicted criminals, or reformants, via their neural mediation implants.
In the early to mid 24th century, the Lisqual and other allied fought a war with other governments on Betrisius. As part of their war effort, the Lisqual government reprogramming their reformants' mediators and conscripted them into the military, calling them Morhenza. Following their victory in the war, the Lisqual returned these Morhenza to reformant status.
When the United Federation of Planets made formal first contact with Betrisius in 2376, the Lisqual were key members of the initial delegation, including a Lisqual woman named Dolanara. Dolanara also felt that the Lisqual were being less than forthcoming in their dealings with Federation representatives regarding their criminal justice system, and in 2377, created multiple disturbances in the reformant community to draw Federation attention to the Lisqual government's policies.
The Lisqual government was headed by a governor, who was advised by a number of ministers. The seat of government was in the city of Gisela. (CoE eBook: Turn the Page)