While there is a whole sport dedicated to summiting the highest point in each state, there is not one for summiting the lowest point in each state. You may assume this is because getting to a state's lowest point isn't really a challenge. However, very few states without access to a coast have easily reachable low points.
One of the inland states where it is possible to summit the low point is Illinois, whose lowest point is located at a 279 foot elevation at Fort Defiance Point, at the confluence of the Mississippi and Ohio rivers. Known as Camp Defiance during the American Civil War, Fort Defiance is a former military fortification. Formerly a State Park, it now is owned and maintained by the city of Cairo, Illinois.