I would have thought builders white, otherwise also referred to as ceiling white would be more like vivid white not lexicon. Lexicon in full strength can look quite blue. We've used Lexicon in halfstrength in my daughters room which I've just posted pictures of so you can have a look. The ceilings are in vivid white which I think is more likely to be what is on your ceiling and cornice. https://www.houzz.com.au/discussions/6100414/wardrobe-renovations#27205610

We looked at natural white when selecting colours but for us it was still too much of a yellow tinge which is why we went for the cooler white, so it's personal preference I think as to which you like.

Builders white refers to untinted vivid white and a standard for ceilings and cornices, although you can paint them in whatever colour you want. Natural white is great neutral on walls, slightly warmer or softer than vivid white without really throwing colour. If you paint walls and ceiling in the same colour, whatever tint, is the least cost of all as no fiddling cutting in on cornice line.

The standard ceiling white will look fine with Natural White walls. The ceiling paint will be more of a Matt finish which takes away some of the starkness of the ceiling white and being Matt it dissent really through under tones. I can’t understand why it would cost more to change if the work hasn’t started. The paint costs the same (or maybe it doesn’t in the builders world). Either way the room will look good.

Thank you everyone for the comments!
Leigh my mistake , the painter said the builders white is like lexicon quarter I think , your daughter’s room looks beautiful , I love the doors too

Builders white is not Ceiling White (which is the base vivid white). Builders white is vivid white a few drops of black and adds practicality when covering a large area, because it tends to cover small marks slightly better. It is still very white, almost unnoticeably different. My understanding is professionals opt for this to improve performance and coverage. It is a better choice for the customer and for the painter. Vivid white is difficult to work with unless you're prepared to do lots of coats. Builders You may find that Lexicon Quarter is the same as builders white: vivid white with a few drops of black. Lexicon quarter is the go to very bright white from dulux. Natural white simply has more black added to it, to take off the stark edge off.

Lexicon is blue especially in dark rooms. I'd keep the ceiling and cornice white (Ceiling white) and natural for the rest like you have planned. This is what I did for my house and it works very well.