I’m pretty sure your 04 is the same front end cap as my 02. Ref the picture.
If you want to replace the bulb only, check these bulb part #:
Headlight high 9005
Headlight low 9006
If you need the whole headlight assembly, here are those Mfgr part numbers:
Headlight assy Right TYC20-5859;
Headlight assy. Left. TYC20-5860
You can save some $$$ by going to your local auto parts and buying the headlight assembly for a 2000-2002 Lincoln LS.