For a physicist, Lab is nice to describe colors we see. For a photographer, it is not nice to apply transformations.
We (and camera sensors) see a trichromatic signal (from 3 different cells, in the eye) and the brain recomposes the lightness by mixing RGB channels. Applying the same transfer function on the 3 RGB channels will actually affect the lightness and the color saturation, but in a “natural way” (for the eye) because the lightness is only a side-effect of the trichromatic manipulation.
In Lab space, the lightness is fully separated from the colors, which could seem nice at first, because you control everything, but will actually result in washed-out results because you need do fix the color saturation according to the lightness in the same way the eye behaves. In the Lab modules of dt (for example : tone curves in auto mode), you adjust the L channel transfer function, and the module will make the assumption that the a & b channels should follow the same function, which is silly because it doesn’t take account of the way we percieve color & lightness. So you will either get desaturated or weirdly saturated color saturation.
Lab is great for special effects, such as creating more color separation, due to the way it represents colors : on the a channel, the more green you are, the less magenta you are, same for blue/yellow on the b channel. So, increasing the contrast in a & b results in more defined colors. But, in portrait, it will just make the spots and blemishes pop out.
90 % of the color, lightness and contrst adjustments should be made (from my taste & experimentations) in RGB, because it’s safe. Once you have got someting natural and good looking, you can run the extra mile in Lab for (delicate) special effects, on separated channels (no auto Lab mode that affects the 3 channels with the same transfer function).
That’s basically how I recovered this picture.