I did a little mock up of a simple lock icon that changes state when you toggle luminosity lock on and off. The things I tried to make the design do were:
1 make both unlocked and locked states have the icon present to differentiate it from other slider handles and suggest in both states that it is tap-able (to help this feature be discoverable)
2 make the same icon work on all the different hue slider handle types (some are transparent, some are opaque, some are on thin bars, others are are on thicker bars)
This icon could be overlaid on the radiating lines that indicate the locked state in the current implementation, but I wasn't sure that those radiating lines would work well with the other thinner hue sliders because they might stick out. It is nice that they change the silhouette though, it might be worth adding to the others for that reason.
I tried changing the shape of the lock icon itself to be "open" in the unlocked state, but opted to just lower its opacity to illustrate the state change because of the constrained space available. I also considered putting a little "L" for luminosity on the lock, but thought it wasn't needed, wouldn't make sense in other languages potentially, and probably wouldn't look as clean.
I also played with darkening the area behind the icon for the locked state which did make it stand out more, but I felt it wasn't necessary and it was better to keep it lighter and let the color show through more.
I hope this is helpful/clear!