The image will be recompressed. The two scenarios you describe are actually effectively the same, because the lossy part of the JPEG compression discards information which stays gone when the image is decompressed. (Hence, lossy.) That means that reapplying with the exact same parameters shouldn't do much, either in terms of further space saves or in terms of further artifacts. The differences come down to precision and rounding errors. (This is the same in Lightroom as it is in any other program.)

So, if you recompress with exact same parameters and have aligned your crop to 8×8 blocks, the degradation should be minimal. However, if you're using a high level of compression (I think 80% qualifies), you might actually see a difference, because the artifacts introduced by the initial compression are permanent changes to the image and will get recompressed too, possibly causing more artifacts.

Setting to 100 will be more safe, as any newly added artifacts will be hard to notice. It won't make the image any better, but not significantly worse. However, it will introduce changes across the whole image, whereas resaving will mostly concentrate changes to where artifacts are already noticeable. This, unfortunately, means that your mileage will vary.

If you're resizing or have made significant manipuations, all bets are off.

See this answer for details on how bad this degradation can get (and how to minimize it).