I'm guessing that I need to do that?? Didn't think LR would require a two step process to write IPTC data.
Well, it depends what type of image you are talking about. At first you said you were dealing with TIF files, then you refer to CaptureOne so it sounds like you're worried about raw files.
Remember that LR is a database and holds the metadata in the database, not appending it to the file each time you enter something. LR writes IPTC data directly into documented file types (psd, jpg, tif, dng) when you export a file, or when you choose that command (or set a preference for continuous writing). For non-documented file types, mainly raw files, you have to generate XMP sidecars and that's done either by that menu command or by the preference.
It then depends on whether the other program can read XMP-format metadata (XMP can be inside the image or in the sidecar). I thought the latest version of PM could do so, Bridge and iView can, but NX will certainly have a problem, as does Aperture. Don't know about C1.
With these things the devil's in the detail so you need to be very precise when you say "Everytime LR is loaded, I can see that IPTC data. Then I open the photos using Photo Mechanic, Capture NX, and a trial version of Capture One. " What format are "the photos" - still raw or tifs? What happens between "data." and "Then...." - do you export or just close LR?