Well, along side the workflow discussion, we still don't know why Lightroom will not recognize your jpeg.
One thing to check on is to name your jpeg in a way that is not the same base name as your Raw file or tiff. Maybe LR is trying to incorporate it as a duplicate image and it doesn't match -- I'm not saying it is or that it's "good", just taking a stab there.
The only other thing that I can think of for now is whether you have the jpeg in a color space that is out-of-whack -- in other words not sRGB, aRGB or ProPhotoRGB, maybe it's been set inadvertently to, say, the monitor profile or some other out-of-norm space that Lightroom doesn't like.
Again, I don't really have the slightest idea, but those are a couple things I would check on. There is no reason for Lightroom to not be able to process a "normal" jpeg.
One thing to check also: can you open the jpeg in Camera Raw through Bridge (open Bridge and right-click on the jpeg and choose Open in Camera Raw)? Camera Raw and Lightroom have the same Raw processing engine so it could give more clues as to what happens.