At what age will Lilly's beak darken to that beautiful glossy black colour? She is 12 going on 13 weeks now if that helps. Or is it not an age thing but a health/diet thing like with ringneck beak colour?

It depends on the bird. Some darken quicker than others. I have a friend whose female did not darken until she was over a year. Usually the are almost totally dark by about 6 months. Hope this helps!

Yes, at about 4-6 months they will get darker. Some mature faster while others are slower, so don't be too worried if it is still light several months past that