These are the recommended lift points for the Mark VIII:
You can also use the points just under where the rear air bags are. Just put a piece of wood in to protect the arms... DO NOT JACK THE CAR UP BY THE REAR DIFFERENTIAL... It is aluminum and will get messed up.
Make sure you turn off the air ride switch in the trunk before you lift the car. Turn it back on when you lower it.
Make sure the car is supported securely on approved locked jacks before you get under the car. Do not get under a car only supported by hydraulic jacks. Working under cars is dangerous. Try to minimize the danger.
Information from the Lincoln Mark VIII shop manual. Thanks to Calvin Louie for finding the information and Mike Gilbert for the additional lift point pointers based on his experience.