You might check the owner's manual to see whether there is a dedicated fuse for the alarm. If there is one, removing it would obviously disable the alarm. Trouble is, the alarm may share its circuit with other components in the car. Maybe the manual will tell you whether there is a diagnostic function for the alarm that may tell you which sensor or output is causing the false alarms. The manual may even tell you how to lock the doors without setting the alarm, maybe try opening the door to get out of the car while the engine is still running, then lock the door, exit the car and close the door? If none of these ideas work, you may need to have the Lincoln dealer scan the computers in the car to see if it will tell what input is causing the false alarms.
I have no idea exactly how the alarm in your car is activated. I do know that most OEM alarms are turned on when the door is locked, either manually or with the keyless entry remote control. According to a car security technical website I have, there is a dark green with a purple stripe wire in the driver's door at the door control module that if you ground it, will disable the OEM alarm. That sounds like a fairly drastic measure to fix this problem though. Maybe the dealer can shed more light on it for you. Good luck with it.