Based on the example and the community replies, Lux appears to be a fairly simple combination of edits rather than some mysterious scene-aware algorithm.

The visible changes are likely:

• increased overall contrast
• slightly higher exposure / brighter midtones
• stronger vibrance or saturation
• more local contrast/clarity for “pop”
• a touch of softening/smoothing

A big part of the improvement may simply be tonal range expansion: making blacks truly black and whites truly white. If your image starts out flat, setting proper black and white points can make it look much livelier right away.

To mimic this in Lightroom, try:

1. Set black and white points so the histogram uses more of the full tonal range.
2. Add a mild S-curve or increase Contrast.
3. Raise Vibrance slightly; use Saturation more carefully.
4. Add a little Clarity or local contrast.
5. If needed, lift exposure or midtones slightly.
6. For portraits, consider very subtle softening to keep skin pleasant.

It’s probably reproducible as a preset, but you’ll still need to tweak per image because exposure and color vary from shot to shot.