I believe most of what you're seeing here is some kind of dithering. It's a common step when writing out processed data where the input data range is much larger than is needed for the final output. It has a way of masking tiny errors that creep in through a processing chain.

I don't think this is anything to worry about. Pretty much every music track produced in the past two decades or so has been dithered during the mix-down process from high resolution masters (e.g. 96 kHz 24-bit per channel) to delivery formats like CD and MP3. You can't hear its presence, though you might hear its absence! Since your ears are more sensitive to small differences than your eyes, I wouldn't worry about any dithering added by Lightroom.

Now, I said "most" of what you're seeing here is the dithering. You're also seeing some artifacts due purely to problems in your test method:

1. JPEG is the wrong format to use when pixel-peeping unless your aim is to look for differences introduced by the JPEG algorithm. JPEG is lossy: a difference in one pixel is likely to affect the values in 63 of its neighbors, however slightly.

2. Divide is the wrong tool for detecting image differences. Suffice it to say, there are several ways for it to give false negatives, which is to say that it can indicate that two pixels are the same when they are different. There is also at least one case I can think of where Divide will indicate that two pixels are different when they are the same!

   A much better choice here is the Difference blend mode. It always gives a pure black image when the upper layer is exactly the same as the layer(s) below it.

   You can also use the Apply Image command to do pixel-level forensics on an image.

   Another superior option is ImageMagick's compare tool.