You've managed to mitigate the issue reasonably well, but we see some of the issues you were facing.
This type of issue is something Lightroom was never designed to handled and is the point where Photoshop and its more advanced selection tools shine. Photoshop has luminosity masking capabilities (the Select Color functionality is where this is buried) makes quick work of this, but there is a steep learning curve.
Thank you, Manfred, for pointing me in that direction. I have access to some pretty good photoshop tutorials on Linkedin Learning which I move in and out off. I will look up select color functionality. A steep climb indeed.
The side of his face is very dark. Can that be improved as well?
Excellent fix, Manfred. You gave me something to work towards.
+1 for using luminosity masks in PS to treat this, but regarding the steep learning curve, I suggest you take a look at Tony Kuyper's web site and the tools he offers for simplifying the use of luminosity masks in Photoshop. I use the free TK6 panel and find it a great help.
https://goodlight.us/
I have tried Kuyper's product and personally find the Photoshop Select Color functionality easier to use and more flexible.
My learning curve comments are meant more for the Lightroom user who generally only uses sliders to make adjustments versus the more complex tools (layers, layer masks and multiple selection approaches).
Lightroom now does luminosity masking. It's fairly sophisticated, although not as controllable as masking in photoshop.
Re luminosity masking in photoshop: my experience is the opposite of Manfred's. Kuyper's product is enormously complex, with multiple panels and many options on each. However, I eventually realized that I need only one relatively simple panel, which he now labels TK8 Multi-Mask. Ignoring the rest makes it far easier to learn. I find that the TK8 MM panel is both very easy to use and very powerful. E.g., if you select by simply clicking one spot, it will create a mask and allow you to change the center, the width, or the whiteness of the mask very easily with sliders, and it also gives you 9 preset ranges you can use as starting points instead.