You can fish from a non-gasoline operated boat. See below from the Lexington Government website, http://www.lexingtonky.gov/index.aspx?page=2078
Jacobson Park Marina
The Jacobson Park Marina has a launch area for non-gasoline powered boats which cost $3 per boat.Patrons may also rent pedal boats which hold two people. The rental cost is $3 for one-half hour. The Jacobson Boat dock typically opens for weekends in late April and opens on a daily basis in late May. All boat riders must wear a US Coast Guard approved personal floatation device. Vending machines and restrooms are available at the Marina. The age requirement for pedal boat rental is 16 & over. Those under the required age must be accompanied by a chaperone 16 or older. Fishing docks are located in several areas throughout the park and are accessible to wheelchairs. You must have a valid Kentucky fishing license if you are 16 or older. There is no charge to fish at this park.