It might be on a sticker on one of the trunk hinges--apparently, they did that on a very few early-build '03 LSes (I know of at least one LS that had it). The only other place the code has been found printed anywhere in the car was on the card that came from the factory. The manual says that it's printed "on the computer," but it's not; the closest any of us have found were the remains of a tag on the DDM that appears to have been torn off at the factory.
If you don't have the hinge sticker or the code card, your only choice is to get it from a dealership. It doesn't have to be Lincoln dealership; you can go to any Ford, Lincoln, or Mercury dealership, or maybe a Mazda dealership, as long as they have an NGS or WDS tester.