So you're talking about the Lens Corrections filter in PS not the Camera Raw plug-in.
The camera model isn't that important for lens corrections because the corrections have been specified in physical distance units (e.g. millimeters or microns or something) not pixels so you can use a lens profile computed from raws shot on one camera for another camera's corrections. You can imagine that Adobe does not create profiles from all lenses on all cameras. That would be 1000s of profiles. Usually there is only camera used to make a profile for a new lens and it's probably the best camera Adobe has access to when the lens profile is created. If you're not seeing a 1D IV in the list that means no new lenses were added for Canon full-frame cameras when the 1D IV was the best full-frame Canon body Adobe had.
The one thing that is important is if your camera is full-frame then you must use a lens profile computed from a full-frame camera (EF), so a lens profile computed from a crop-frame camera (EF-S) should not be used on a full frame camera because there isn't enough data for the outer area of the sensor. It is ok to use a lens profile from a full-frame camera for corrections of a crop-frame camera photos, just not crop-frame profile on a full-frame camera.
So to choose a profile for your Canon 1D IV select Camera Make: Canon, Camera Model: All, Lens Model: whatever lens, and if more than one profile shows up in the list underneath pick the newer full-frame camera as the model to use.
If you're on the prior version, the lens metadata wasn't parsed properly.