I don't know LR, but in PS there are several ways to do it, as there are several ways to do most things. In my opinion, the best is to use a brightness adjustment layer with a layer mask. You can look this up, but here are the basic steps:
1. Create adjustment layer for brightness - there should be an icon on the layers palette to create an adjustment layer, then you select brightness from the list.
2. Use the slider to increase/decrease brightness by about the amount you want for a particular area (you'll need two separate layers to both brighten and darken). Don't fuss at this point - all completely adjustable later.
3. Go to Edit>Fill, then select black to fill the layer with black - this blocks the effect of the adjustment.
4. Select the brush tool, adjust brush size to a little smaller than the area you want to adjust, make the foreground color white, and paint white on the adjustment layer where you want the effect - you should see the image brighten/darken as you do this.
You can adjust or redo the painting on the layer mask or adjust the amount of brightness reduction/increase any time or just delete the entire adjustment layer and start over if you want.