To locate ignition coil 4, you'll need to refer to a repair manual specific to your Lincoln LS's year and engine (there are a few different engines that were offered). The manual will have a diagram showing the cylinder numbering and the corresponding coil location. The firing order is crucial to correctly identify cylinder #4 and its associated coil.
Without knowing the year and engine, I can't give you a precise visual location. However, generally, all the coils will be near the top of the engine, directly above their respective spark plugs.