I am reopening this post with a bit of other info.
Ran the unit today. After a while the fan dropped off and then immediately back on. Had other things to do bit after 4 hours, went in and the unit was running and the unit was cooling and near it's set point. When I turned it to the "OFF" position the compressor quit and the fan continued to run as it should. After 5 minutes the fan was still running so I put the thermostat in the "off" position. It ran for a few minutes and then shutdown as it should. Thermostat fan speed was in AUTO. There does not appear to be any difference in the fan speed or sound when put in the HI or Lo. position.
Dies it sound like a thermostat problem? If so, would a normal thermostat work? I see 3 wires. Orange, white and red.
There thermostat is the original Dometic LCD.