My husband and I have a Lennoxx AC/ Heating Unit that is run by electric. The unit outside will not stop running even though the thermostat is turned off. I have turned off the breaker for now. Any idea what could be causing this ?

Good chance it is a stuck contactor that will need to be replaced.

Most likely. Before replacing it, I would at least make sure you don't have power to the coil. A new contactor is a simple DIY project. Shut the power off, remove the wires, and carefully transfer them to the same positions on the new one.