What is the best method in Lightroom for removing shine from someone's face that is highlighted in only certain areas. I have come across the skin smoothing tool but it just lowers the clarity and doesn't create a nice appearance.
Depending on the extent of the shine, reducing the Highlights or Whites sliders can help with undesirably shiny skin.
Another technique for reducing brightness in a specific part of the image is to reduce the luminance for a particular color in the photo. You can you use the "HSL" panel and select "Luminance" and dial down the luminance of the color or colors that correspond to the skin tones of your subject. This technique is also useful for making blue skies appear more deep and balanced, rather than washed out.
However, if you've truly blown the highlights (eg, highlights are clipping in the image histogram) then you may need to use a more targeted tool such a spot removal tool to manually tweak the shiny areas on your subjects.
Does Lightroom have a way to apply effects to areas of a photo based on drawn masks (bezier curves, etc) and parametric masks (R, G, B, Y values)?
I use an open source RAW processing program called Darktable which allows me to apply an extra Exposure operation to the areas on the image that fall within a (bright) pixel brightness range, with the exposure set to a negative value. You have to decide the best way to measure pixel brightness (Y, R, G, B), how to specify the softness of the range, and how much darkening can work and still look natural.
I know LR has some capability of reconstructing semi-blown-out highlights, which is also critical to this.
Such retouching is not the strong point of Lightroom. It is designed to do general adjustments to the whole image - a local manipulation is therefore difficult to apply using Lightroom.
Photoshop however is built for those tasks.
There are many elaborate techniques to soften skin, but you might want to try the spot healing brush (and the clone tool) as well as the mixer brush (whom you have to play with).
If you have to much time on your hands, you could take a look at a technique called "frequency seperation".